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Mathematics Subject Classification – Algebra

ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES

AMS: 06       All of this section
AMS: 06-XX    Not classified at a more specific level

• AMS: 06-01    Instructional exposition
• AMS: 06-02    Research exposition
• AMS: 06-03    Historical
• AMS: 06-04    Explicit machine computation and programs
• AMS: 06-06    Proceedings, conferences, collections, etc.

• AMS: 06Axx    Ordered sets
  AMS: 06A*     (including sub-levels)
  • AMS: 06A06    Partial order, general
  • AMS: 06A07    Combinatorics of partially ordered sets
• AMS: 06Bxx    Lattices
  AMS: 06B*     (including sub-levels)
  • AMS: 06B05    Structure theory
  • AMS: 06B15    Representation theory
  • AMS: 06B25    Free lattices, projective lattices, word problems
  • AMS: 06B30    Topological lattices, order topologies
  • AMS: 06B35    Continuous lattices and posets, applications
• AMS: 06Cxx    Modular lattices, complemented lattices
  AMS: 06C*     (including sub-levels)
  • AMS: 06C20    Complemented modular lattices, continuous geometries
• AMS: 06Dxx    Distributive lattices
  AMS: 06D*     (including sub-levels)
• AMS: 06Exx    Boolean algebras (Boolean rings)
  AMS: 06E*     (including sub-levels)
  • AMS: 06E05    Structure theory
  • AMS: 06E30    Boolean functions
• AMS: 06Fxx    Ordered structures
  AMS: 06F*     (including sub-levels)
  • AMS: 06F05    Ordered semigroups and monoids
  • AMS: 06F07    Quantales
  • AMS: 06F15    Ordered groups
  • AMS: 06F20    Ordered abelian groups, Riesz groups, ordered linear spaces
  • AMS: 06F30    Topological lattices, order topologies

GENERAL ALGEBRAIC SYSTEMS

AMS: 08       All of this section
AMS: 08-XX    Not classified at a more specific level

• AMS: 08-01    Instructional exposition
• AMS: 08-02    Research exposition
• AMS: 08-04    Explicit machine computation and programs
• AMS: 08-06    Proceedings, conferences, collections, etc.

• AMS: 08Axx    Algebraic structures
  AMS: 08A*     (including sub-levels)
  • AMS: 08A05    Structure theory
  • AMS: 08A30    Subalgebras, congruence relations
  • AMS: 08A35    Automorphisms, endomorphisms
  • AMS: 08A50    Word problems
• AMS: 08Bxx    Varieties
  AMS: 08B*     (including sub-levels)
  • AMS: 08B10    Congruence modularity, congruence distributivity
  • AMS: 08B25    Products, amalgamated products, and other kinds of limits and colimits
  • AMS: 08B99    None of the above, but in this section
• AMS: 08Cxx    Other classes of algebras
  AMS: 08C*     (including sub-levels)
  • AMS: 08C10    Axiomatic model classes
  • AMS: 08C15    Quasivarieties

NUMBER THEORY

AMS: 11       All of this section
AMS: 11-XX    Not classified at a more specific level

• AMS: 11-00    General reference works
• AMS: 11-01    Instructional exposition
• AMS: 11-02    Research exposition
• AMS: 11-03    Historical
• AMS: 11-04    Explicit machine computation and programs
• AMS: 11-06    Proceedings, conferences, collections, etc.

• AMS: 11Axx    Elementary number theory
  AMS: 11A*     (including sub-levels)
  • AMS: 11A05    Multiplicative structure; Euclidean algorithm; greatest common divisors
  • AMS: 11A07    Congruences; primitive roots; residue systems
  • AMS: 11A15    Power residues, reciprocity
  • AMS: 11A25    Arithmetic functions; related numbers; inversion formulas
  • AMS: 11A41    Primes
  • AMS: 11A51    Factorization; primality
  • AMS: 11A55    Continued fractions
  • AMS: 11A63    Radix representation; digital problems
• AMS: 11Bxx    Sequences and sets
  AMS: 11B*     (including sub-levels)
  • AMS: 11B25    Arithmetic progressions
  • AMS: 11B37    Recurrences
  • AMS: 11B39    Fibonacci and Lucas numbers and polynomials and generalizations
  • AMS: 11B65    Binomial coefficients; factorials; $q$-identities
  • AMS: 11B68    Bernoulli and Euler numbers and polynomials
  • AMS: 11B85    Automata sequences
• AMS: 11Cxx    Polynomials and matrices
  AMS: 11C*     (including sub-levels)
  • AMS: 11C08    Polynomials
  • AMS: 11C20    Matrices, determinants
  • AMS: 11C99    None of the above, but in this section
• AMS: 11Dxx    Diophantine equations
  AMS: 11D*     (including sub-levels)
  • AMS: 11D04    Linear equations
  • AMS: 11D09    Quadratic and bilinear equations
  • AMS: 11D25    Cubic and quartic equations
  • AMS: 11D41    Higher degree equations; Fermat's equation
  • AMS: 11D45    Counting solutions of Diophantine equations
  • AMS: 11D61    Exponential equations
  • AMS: 11D72    Equations in many variables
  • AMS: 11D75    Diophantine inequalities
  • AMS: 11D85    Representation problems
  • AMS: 11D88    $p$-adic and power series fields
  • AMS: 11D99    None of the above, but in this section
• AMS: 11Exx    Forms and linear algebraic groups
  AMS: 11E*     (including sub-levels)
  • AMS: 11E04    Quadratic forms over general fields
  • AMS: 11E08    Quadratic forms over local rings and fields
  • AMS: 11E10    Forms over real fields
  • AMS: 11E12    Quadratic forms over global rings and fields
  • AMS: 11E16    General binary quadratic forms
  • AMS: 11E25    Sums of squares and representations by other particular quadratic forms
  • AMS: 11E39    Bilinear and Hermitian forms
  • AMS: 11E41    Class numbers of quadratic and Hermitian forms
  • AMS: 11E45    Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
  • AMS: 11E57    Classical groups
  • AMS: 11E72    Galois cohomology of linear algebraic groups
  • AMS: 11E81    Algebraic theory of quadratic forms; Witt groups and rings
  • AMS: 11E88    Quadratic spaces; Clifford algebras
  • AMS: 11E95    $p$-adic theory
• AMS: 11Fxx    Discontinuous groups and automorphic forms
  AMS: 11F*     (including sub-levels)
  • AMS: 11F03    Modular and automorphic functions
  • AMS: 11F06    Structure of modular groups and generalizations; arithmetic groups
  • AMS: 11F11    Modular forms, one variable
  • AMS: 11F12    Automorphic forms, one variable
  • AMS: 11F25    Hecke-Petersson operators, differential operators (one variable)
  • AMS: 11F27    Theta series; Weil representation
  • AMS: 11F30    Fourier coefficients of automorphic forms
  • AMS: 11F32    Modular correspondences, etc.
  • AMS: 11F33    Congruences for modular and $p$-adic modular forms
  • AMS: 11F37    Forms of half-integer weight; nonholomorphic modular forms
  • AMS: 11F41    Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
  • AMS: 11F46    Siegel modular groups and their modular and automorphic forms
  • AMS: 11F50    Jacobi forms
  • AMS: 11F55    Other groups and their modular and automorphic forms (several variables)
  • AMS: 11F60    Hecke-Petersson operators, differential operators (several variables)
  • AMS: 11F66    Dirichlet series and functional equations in connection with modular forms
  • AMS: 11F67    Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
  • AMS: 11F70    Representation-theoretic methods; automorphic representations over local and global fields
  • AMS: 11F72    Spectral theory; Selberg trace formula
  • AMS: 11F75    Cohomology of arithmetic groups
  • AMS: 11F80    Galois representations
  • AMS: 11F85    $p$-adic theory, local fields
  • AMS: 11F99    None of the above, but in this section
• AMS: 11Gxx    Arithmetic algebraic geometry (Diophantine geometry)
  AMS: 11G*     (including sub-levels)
  • AMS: 11G05    Elliptic curves over global fields
  • AMS: 11G07    Elliptic curves over local fields
  • AMS: 11G09    Drinfeld modules; higher-dimensional motives, etc.
  • AMS: 11G10    Abelian varieties of dimension $\gtr 1$
  • AMS: 11G15    Complex multiplication and moduli of abelian varieties
  • AMS: 11G16    Elliptic and modular units
  • AMS: 11G18    Arithmetic aspects of modular and Shimura varieties
  • AMS: 11G20    Curves over finite and local fields
  • AMS: 11G25    Varieties over finite and local fields
  • AMS: 11G30    Curves of arbitrary genus or genus $\ne 1$ over global fields
  • AMS: 11G35    Varieties over global fields
  • AMS: 11G40    $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
  • AMS: 11G45    Geometric class field theory
  • AMS: 11G50    Heights
  • AMS: 11G55    Polylogarithms and relations with $K$-theory
  • AMS: 11G99    None of the above, but in this section
• AMS: 11Hxx    Geometry of numbers
  AMS: 11H*     (including sub-levels)
  • AMS: 11H06    Lattices and convex bodies
  • AMS: 11h21    Lattice packing and covering
  • AMS: 11H50    Minima of forms
  • AMS: 11H55    Quadratic forms (reduction theory, extreme forms, etc.)
  • AMS: 11H56    Automorphism groups of lattices
  • AMS: 11H71    Relations with coding theory
  • AMS: 11H99    None of the above, but in this section
• AMS: 11Jxx    Diophantine approximation, transcendental number theory
  AMS: 11J*     (including sub-levels)
  • AMS: 11J20    Inhomogeneous linear forms
  • AMS: 11J61    Approximation in non-Archimedean valuations
  • AMS: 11J68    Approximation to algebraic numbers
  • AMS: 11J70    Continued fractions and generalizations
  • AMS: 11J71    Distribution modulo one
  • AMS: 11J72    Irrationality; linear independence over a field
  • AMS: 11J82    Measures of irrationality and of transcendence
  • AMS: 11J83    Metric theory
  • AMS: 11J85    Algebraic independence; Gelfond's method
  • AMS: 11J91    Transcendence theory of other special functions
  • AMS: 11J99    None of the above, but in this section
• AMS: 11Kxx    Probabilistic theory: distribution modulo $1$; metric theory of algorithms
  AMS: 11K*     (including sub-levels)
  • AMS: 11K16    Normal numbers, radix expansions, etc.
  • AMS: 11K38    Irregularities of distribution, discrepancy
  • AMS: 11K41    Continuous, $p$-adic and abstract analogues
  • AMS: 11K45    Pseudo-random numbers; Monte Carlo methods
  • AMS: 11K50    Metric theory of continued fractions
  • AMS: 11K55    Metric theory of other algorithms and expansions; measure and Hausdorff dimension
  • AMS: 11K60    Diophantine approximation
  • AMS: 11K65    Arithmetic functions
  • AMS: 11K70    Harmonic analysis and almost periodicity
• AMS: 11Lxx    Exponential sums and character sums
  AMS: 11L*     (including sub-levels)
  • AMS: 11L40    Estimates on character sums
• AMS: 11Mxx    Zeta and $L$-functions: analytic theory
  AMS: 11M*     (including sub-levels)
  • AMS: 11M06    $\zeta (s)$ and $L(s, \chi)$
  • AMS: 11M20    Real zeros of $L(s, \chi)$; results on $L(1, \chi)$
  • AMS: 11M26    Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
  • AMS: 11M36    Selberg zeta functions and regularized determinants
  • AMS: 11M38    Zeta and $L$-functions in characteristic $p$
  • AMS: 11M41    Other Dirichlet series and zeta functions
  • AMS: 11M45    Tauberian theorems
• AMS: 11Nxx    Multiplicative number theory
  AMS: 11N*     (including sub-levels)
  • AMS: 11N05    Distribution of primes
  • AMS: 11N13    Primes in progressions
  • AMS: 11N25    Distribution of integers with specified multiplicative constraints
  • AMS: 11N35    Sieves
  • AMS: 11N36    Applications of sieve methods
  • AMS: 11N37    Asymptotic results on arithmetic functions
  • AMS: 11N75    Applications of automorphic functions and forms to multiplicative problems
  • AMS: 11N99    None of the above, but in this section
• AMS: 11Pxx    Additive number theory; partitions
  AMS: 11P*     (including sub-levels)
  • AMS: 11P05    Waring's problem and variants
  • AMS: 11P21    Lattice points in specified regions
  • AMS: 11P32    Goldbach-type theorems; other additive questions involving primes
  • AMS: 11P55    Applications of the Hardy-Littlewood method
  • AMS: 11P81    Elementary theory of partitions
  • AMS: 11P82    Analytic theory of partitions
  • AMS: 11P83    Partitions; congruences and congruential restrictions
• AMS: 11Rxx    Algebraic number theory: global fields
  AMS: 11R*     (including sub-levels)
  • AMS: 11R04    Algebraic numbers; rings of algebraic integers
  • AMS: 11R06    PV-numbers and generalizations; other special algebraic numbers
  • AMS: 11R09    Polynomials (irreducibility, etc.)
  • AMS: 11R11    Quadratic extensions
  • AMS: 11R18    Cyclotomic extensions
  • AMS: 11R21    Other number fields
  • AMS: 11R23    Iwasawa theory
  • AMS: 11R27    Units and factorization
  • AMS: 11R29    Class numbers, class groups, discriminants
  • AMS: 11R32    Galois theory
  • AMS: 11R33    Integral representations related to algebraic numbers; Galois module structure of rings of integers
  • AMS: 11R34    Galois cohomology
  • AMS: 11R37    Class field theory
  • AMS: 11R39    Langlands-Weil conjectures, nonabelian class field theory
  • AMS: 11R42    Zeta functions and $L$-functions of number fields
  • AMS: 11R44    Distribution of prime ideals
  • AMS: 11R47    Other analytic theory
  • AMS: 11R52    Quaternion and other division algebras: arithmetic, zeta functions
  • AMS: 11R54    Other algebras and orders, and their zeta and $L$-functions
  • AMS: 11R56    Adele rings and groups
  • AMS: 11R58    Arithmetic theory of algebraic function fields
  • AMS: 11R70    $K$-theory of global fields
  • AMS: 11R80    Totally real and totally positive fields
  • AMS: 11R99    None of the above, but in this section
• AMS: 11Sxx    Algebraic number theory: local and $p$-adic fields
  AMS: 11S*     (including sub-levels)
  • AMS: 11S05    Polynomials
  • AMS: 11S15    Ramification and extension theory
  • AMS: 11S20    Galois theory
  • AMS: 11S23    Integral representations
  • AMS: 11S25    Galois cohomology
  • AMS: 11S31    Class field theory; $p$-adic formal groups
  • AMS: 11S37    Langlands-Weil conjectures, nonabelian class field theory
  • AMS: 11S40    Zeta functions and $L$-functions
  • AMS: 11S45    Algebras and orders, and their zeta functions
  • AMS: 11S70    $K$-theory of local fields
  • AMS: 11S80    Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
  • AMS: 11S85    Other nonanalytic theory
  • AMS: 11S99    None of the above, but in this section
• AMS: 11Txx    Finite fields and commutative rings (number-theoretic aspects)
  AMS: 11T*     (including sub-levels)
  • AMS: 11T06    Polynomials
  • AMS: 11T23    Exponential sums
  • AMS: 11T24    Other character sums and Gauss sums
  • AMS: 11T30    Structure theory
  • AMS: 11T55    Arithmetic theory of polynomial rings over finite fields
  • AMS: 11T60    Finite upper half-planes
  • AMS: 11T71    Algebraic coding theory; cryptography
• AMS: 11Uxx    Connections with logic
  AMS: 11U*     (including sub-levels)
  • AMS: 11U05    Decidability
  • AMS: 11U09    Model theory
  • AMS: 11U10    Nonstandard arithmetic
• AMS: 11Yxx    Computational number theory
  AMS: 11Y*     (including sub-levels)
  • AMS: 11Y05    Factorization
  • AMS: 11Y11    Primality
  • AMS: 11Y16    Algorithms; complexity
  • AMS: 11Y35    Analytic computations
  • AMS: 11Y40    Algebraic number theory computations
  • AMS: 11Y60    Evaluation of constants
• AMS: 11Zxx    Miscellaneous applications of number theory
  AMS: 11Z*     (including sub-levels)
  • AMS: 11Z05    Miscellaneous applications of number theory

FIELD THEORY AND POLYNOMIALS

AMS: 12       All of this section
AMS: 12-XX    Not classified at a more specific level

• AMS: 12-01    Instructional exposition
• AMS: 12-02    Research exposition
• AMS: 12-03    Historical
• AMS: 12-04    Explicit machine computation and programs
• AMS: 12-06    Proceedings, conferences, collections, etc.

• AMS: 12Dxx    Real and complex fields
  AMS: 12D*     (including sub-levels)
  • AMS: 12D05    Polynomials: factorization
  • AMS: 12D15    Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
• AMS: 12Exx    General field theory
  AMS: 12E*     (including sub-levels)
  • AMS: 12E05    Polynomials (irreducibility, etc.)
  • AMS: 12E15    Skew fields, division rings
  • AMS: 12E25    Hilbertian fields; Hilbert's irreducibility theorem
  • AMS: 12E30    Field arithmetic
• AMS: 12Fxx    Field extensions
  AMS: 12F*     (including sub-levels)
  • AMS: 12F05    Algebraic extensions
  • AMS: 12F10    Separable extensions, Galois theory
  • AMS: 12F12    Inverse Galois theory
  • AMS: 12F20    Transcendental extensions
• AMS: 12Gxx    Homological methods (field theory)
  AMS: 12G*     (including sub-levels)
  • AMS: 12G05    Galois cohomology
• AMS: 12Hxx    Differential and difference algebra
  AMS: 12H*     (including sub-levels)
  • AMS: 12H05    Differential algebra
  • AMS: 12H10    Difference algebra
  • AMS: 12h20    Abstract differential equations
  • AMS: 12h25    $p$-adic differential equations
• AMS: 12Jxx    Topological fields
  AMS: 12J*     (including sub-levels)
  • AMS: 12J10    Valued fields
  • AMS: 12J15    Ordered fields
  • AMS: 12J20    General valuation theory
  • AMS: 12J25    Non-Archimedean valued fields
  • AMS: 12J99    None of the above, but in this section
• AMS: 12Kxx    Generalizations of fields
  AMS: 12K*     (including sub-levels)
• AMS: 12Lxx    Connections with logic
  AMS: 12L*     (including sub-levels)
  • AMS: 12L05    Decidability
  • AMS: 12L10    Ultraproducts
  • AMS: 12L12    Model theory
  • AMS: 12L15    Nonstandard arithmetic
• AMS: 12Yxx    Computational aspects of field theory and polynomials
  AMS: 12Y*     (including sub-levels)
  • AMS: 12Y05    Computational aspects of field theory and polynomials

COMMUTATIVE RINGS AND ALGEBRAS

AMS: 13       All of this section
AMS: 13-XX    Not classified at a more specific level

• AMS: 13-01    Instructional exposition
• AMS: 13-02    Research exposition
• AMS: 13-04    Explicit machine computation and programs
• AMS: 13-06    Proceedings, conferences, collections, etc.

• AMS: 13Axx    General commutative ring theory
  AMS: 13A*     (including sub-levels)
  • AMS: 13A02    Graded rings
  • AMS: 13A15    Ideals; multiplicative ideal theory
  • AMS: 13A18    Valuations and their generalizations
  • AMS: 13A30    Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
  • AMS: 13A50    Actions of groups on commutative rings; invariant theory
  • AMS: 13A99    None of the above, but in this section
• AMS: 13Bxx    Ring extensions and related topics
  AMS: 13B*     (including sub-levels)
  • AMS: 13B05    Galois theory
  • AMS: 13B10    Morphisms
  • AMS: 13B22    Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)
  • AMS: 13B25    Polynomials over commutative rings
  • AMS: 13B40    Étale and flat extensions; Henselization; Artin approximation
  • AMS: 13B99    None of the above, but in this section
• AMS: 13Cxx    Theory of modules and ideals
  AMS: 13C*     (including sub-levels)
  • AMS: 13C05    Structure, classification theorems
  • AMS: 13C10    Projective and free modules and ideals
  • AMS: 13C14    Cohen-Macaulay modules
  • AMS: 13C15    Dimension theory, depth, related rings (catenary, etc.)
  • AMS: 13C40    Linkage, complete intersections and determinantal ideals
  • AMS: 13C99    None of the above, but in this section
• AMS: 13Dxx    Homological methods
  AMS: 13D*     (including sub-levels)
  • AMS: 13D02    Syzygies and resolutions
  • AMS: 13D03    (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
  • AMS: 13D05    Homological dimension
  • AMS: 13D10    Deformations and infinitesimal methods
  • AMS: 13D15    Grothendieck groups, $K$-theory
  • AMS: 13D22    Homological conjectures (intersection theorems)
  • AMS: 13D30    Torsion theory
  • AMS: 13D40    Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
  • AMS: 13D45    Local cohomology
  • AMS: 13D99    None of the above, but in this section
• AMS: 13Exx    Chain conditions, finiteness conditions
  AMS: 13E*     (including sub-levels)
  • AMS: 13E05    Noetherian rings and modules
  • AMS: 13E10    Artinian rings and modules, finite-dimensional algebras
  • AMS: 13E15    Rings and modules of finite generation or presentation; number of generators
  • AMS: 13E99    None of the above, but in this section
• AMS: 13Fxx    Arithmetic rings and other special rings
  AMS: 13F*     (including sub-levels)
  • AMS: 13F05    Dedekind, Prüfer and Krull rings and their generalizations
  • AMS: 13F10    Principal ideal rings
  • AMS: 13F15    Factorial rings, unique factorization domains
  • AMS: 13F20    Polynomial rings and ideals; rings of integer-valued polynomials
  • AMS: 13F25    Formal power series rings
  • AMS: 13F45    Seminormal rings
  • AMS: 13F50    Rings with straightening laws, Hodge algebras
  • AMS: 13F55    Face and Stanley-Reisner rings; simplicial complexes
  • AMS: 13F99    None of the above, but in this section
• AMS: 13Gxx    Integral domains
  AMS: 13G*     (including sub-levels)
  • AMS: 13G05    Integral domains
• AMS: 13Hxx    Local rings and semilocal rings
  AMS: 13H*     (including sub-levels)
  • AMS: 13H05    Regular local rings
  • AMS: 13H10    Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
  • AMS: 13H15    Multiplicity theory and related topics
  • AMS: 13H99    None of the above, but in this section
• AMS: 13Jxx    Topological rings and modules
  AMS: 13J*     (including sub-levels)
  • AMS: 13J05    Power series rings
  • AMS: 13J07    Analytical algebras and rings
• AMS: 13Lxx    Applications of logic to commutative algebra
  AMS: 13L*     (including sub-levels)
  • AMS: 13L05    Applications of logic to commutative algebra
• AMS: 13Mxx    Finite commutative rings
  AMS: 13M*     (including sub-levels)
  • AMS: 13M10    Polynomials
• AMS: 13Nxx    Differential algebra
  AMS: 13N*     (including sub-levels)
  • AMS: 13N05    Modules of differentials
  • AMS: 13N10    Rings of differential operators and their modules
  • AMS: 13N99    None of the above, but in this section
• AMS: 13Pxx    Computational aspects of commutative algebra
  AMS: 13P*     (including sub-levels)
  • AMS: 13P05    Polynomials, factorization
  • AMS: 13P10    Polynomial ideals, Gröbner bases
  • AMS: 13P20    Computational homological algebra

ALGEBRAIC GEOMETRY

AMS: 14       All of this section
AMS: 14-XX    Not classified at a more specific level

• AMS: 14-01    Instructional exposition
• AMS: 14-02    Research exposition
• AMS: 14-03    Historical
• AMS: 14-04    Explicit machine computation and programs
• AMS: 14-06    Proceedings, conferences, collections, etc.

• AMS: 14Axx    Foundations
  AMS: 14A*     (including sub-levels)
  • AMS: 14A05    Relevant commutative algebra
  • AMS: 14A10    Varieties and morphisms
  • AMS: 14A15    Schemes and morphisms
  • AMS: 14A20    Generalizations (algebraic spaces, stacks)
  • AMS: 14A22    Noncommutative algebraic geometry
  • AMS: 14A99    None of the above, but in this section
• AMS: 14Bxx    Local theory
  AMS: 14B*     (including sub-levels)
  • AMS: 14B05    Singularities
  • AMS: 14B07    Deformations of singularities
  • AMS: 14B10    Infinitesimal methods
  • AMS: 14B12    Local deformation theory, Artin approximation, etc.
  • AMS: 14B15    Local cohomology
  • AMS: 14B20    Formal neighborhoods
  • AMS: 14B25    Local structure of morphisms: étale, flat, etc.
  • AMS: 14B99    None of the above, but in this section
• AMS: 14Cxx    Cycles and subschemes
  AMS: 14C*     (including sub-levels)
  • AMS: 14C05    Parametrization (Chow and Hilbert schemes)
  • AMS: 14C15    Chow groups and rings
  • AMS: 14C17    Intersection theory, characteristic classes, intersection multiplicities
  • AMS: 14C20    Divisors, linear systems, invertible sheaves
  • AMS: 14C22    Picard groups
  • AMS: 14C25    Algebraic cycles
  • AMS: 14C30    Transcendental methods, Hodge theory , Hodge conjecture
  • AMS: 14C34    Torelli problem
  • AMS: 14C35    Applications of methods of algebraic $K$-theory
  • AMS: 14C40    Riemann-Roch theorems
  • AMS: 14C99    None of the above, but in this section
• AMS: 14Dxx    Families, fibrations
  AMS: 14D*     (including sub-levels)
  • AMS: 14D05    Structure of families (Picard-Lefschetz, monodromy, etc.)
  • AMS: 14D07    Variation of Hodge structures
  • AMS: 14D10    Arithmetic ground fields (finite, local, global)
  • AMS: 14D15    Formal methods; deformations
  • AMS: 14D20    Algebraic moduli problems, moduli of vector bundles
  • AMS: 14D21    Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
  • AMS: 14D22    Fine and coarse moduli spaces
  • AMS: 14D99    None of the above, but in this section
• AMS: 14Exx    Birational geometry
  AMS: 14E*     (including sub-levels)
  • AMS: 14E05    Rational and birational maps
  • AMS: 14E07    Birational automorphisms, Cremona group and generalizations
  • AMS: 14E15    Global theory and resolution of singularities
  • AMS: 14E20    Coverings
  • AMS: 14E22    Ramification problems
  • AMS: 14E25    Embeddings
  • AMS: 14E30    Minimal model program (Mori theory, extremal rays)
  • AMS: 14E99    None of the above, but in this section
• AMS: 14Fxx    (Co)homology theory
  AMS: 14F*     (including sub-levels)
  • AMS: 14F05    Vector bundles, sheaves, related constructions
  • AMS: 14F10    Differentials and other special sheaves
  • AMS: 14F17    Vanishing theorems
  • AMS: 14F20    Étale and other Grothendieck topologies and cohomologies
  • AMS: 14F25    Classical real and complex cohomology
  • AMS: 14F30    $p$-adic cohomology, crystalline cohomology
  • AMS: 14F35    Homotopy theory; fundamental groups
  • AMS: 14F40    de Rham cohomology
  • AMS: 14F42    Motivic cohomology
  • AMS: 14F45    Topological properties
  • AMS: 14F99    None of the above, but in this section
• AMS: 14Gxx    Arithmetic problems. Diophantine geometry
  AMS: 14G*     (including sub-levels)
  • AMS: 14G05    Rational points
  • AMS: 14G10    Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)
  • AMS: 14G15    Finite ground fields
  • AMS: 14G20    Local ground fields
  • AMS: 14G22    Rigid analytic geometry
  • AMS: 14G25    Global ground fields
  • AMS: 14G35    Modular and Shimura varieties
  • AMS: 14G40    Arithmetic varieties and schemes; Arakelov theory; heights
  • AMS: 14G50    Applications to coding theory and cryptography
  • AMS: 14G99    None of the above, but in this section
• AMS: 14Hxx    Curves
  AMS: 14H*     (including sub-levels)
  • AMS: 14H05    Algebraic functions; function fields
  • AMS: 14H10    Families, moduli (algebraic)
  • AMS: 14H15    Families, moduli (analytic)
  • AMS: 14h20    Singularities, local rings
  • AMS: 14h25    Arithmetic ground fields
  • AMS: 14h20    Coverings, fundamental group
  • AMS: 14h27    Automorphisms
  • AMS: 14H40    Jacobians, Prym varieties
  • AMS: 14H42    Theta functions; Schottky problem
  • AMS: 14H45    Special curves and curves of low genus
  • AMS: 14H50    Plane and space curves
  • AMS: 14H52    Elliptic curves
  • AMS: 14H55    Riemann surfaces; Weierstrass points; gap sequences
  • AMS: 14H60    Vector bundles on curves and their moduli
  • AMS: 14H70    Relationships with integrable systems
  • AMS: 14H81    Relationships with physics
  • AMS: 14H99    None of the above, but in this section
• AMS: 14Jxx    Surfaces and higher-dimensional varieties
  AMS: 14J*     (including sub-levels)
  • AMS: 14J10    Families, moduli, classification: algebraic theory
  • AMS: 14J15    Moduli, classification: analytic theory; relations with modular forms
  • AMS: 14J17    Singularities
  • AMS: 14J20    Arithmetic ground fields
  • AMS: 14J25    Special surfaces
  • AMS: 14J26    Rational and ruled surfaces
  • AMS: 14J27    Elliptic surfaces
  • AMS: 14J28    $K3$ surfaces and Enriques surfaces
  • AMS: 14J29    Surfaces of general type
  • AMS: 14J30    $3$-folds
  • AMS: 14J32    Calabi-Yau manifolds, mirror symmetry
  • AMS: 14J33    Mirror symmetry
  • AMS: 14J35    $4$-folds
  • AMS: 14J40    $n$-folds ($n>4$)
  • AMS: 14J45    Fano varieties
  • AMS: 14J50    Automorphisms of surfaces and higher-dimensional varieties
  • AMS: 14J60    Vector bundles on surfaces and higher-dimensional varieties, and their moduli
  • AMS: 14J70    Hypersurfaces
  • AMS: 14J80    Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
  • AMS: 14J81    Relationships with physics
  • AMS: 14J99    None of the above, but in this section
• AMS: 14Kxx    Abelian varieties and schemes
  AMS: 14K*     (including sub-levels)
  • AMS: 14K05    Algebraic theory
  • AMS: 14K10    Algebraic moduli, classification
  • AMS: 14K12    Subvarieties
  • AMS: 14K15    Arithmetic ground fields
  • AMS: 14K20    Analytic theory; abelian integrals and differentials
  • AMS: 14K22    Complex multiplication
  • AMS: 14K25    Theta functions
  • AMS: 14K30    Picard schemes, higher Jacobians
  • AMS: 14K99    None of the above, but in this section
• AMS: 14Lxx    Algebraic groups
  AMS: 14L*     (including sub-levels)
  • AMS: 14L05    Formal groups, $p$-divisible groups
  • AMS: 14L10    Group varieties
  • AMS: 14L15    Group schemes
  • AMS: 14L17    Affine algebraic groups, hyperalgebra constructions
  • AMS: 14L24    Geometric invariant theory
  • AMS: 14L30    Group actions on varieties or schemes (quotients)
  • AMS: 14L35    Classical groups (geometric aspects)
  • AMS: 14L40    Other algebraic groups (geometric aspects)
  • AMS: 14L99    None of the above, but in this section
• AMS: 14Mxx    Special varieties
  AMS: 14M*     (including sub-levels)
  • AMS: 14M05    Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
  • AMS: 14M06    Linkage
  • AMS: 14M07    Low codimension problems
  • AMS: 14M10    Complete intersections
  • AMS: 14M12    Determinantal varieties
  • AMS: 14M15    Grassmannians, Schubert varieties, flag manifolds
  • AMS: 14M17    Homogeneous spaces and generalizations
  • AMS: 14M20    Rational and unirational varieties
  • AMS: 14M25    Toric varieties, Newton polyhedra
  • AMS: 14M99    None of the above, but in this section
• AMS: 14Nxx    Projective and enumerative geometry
  AMS: 14N*     (including sub-levels)
  • AMS: 14N05    Projective techniques
  • AMS: 14N10    Enumerative problems (combinatorial problems)
  • AMS: 14N15    Classical problems, Schubert calculus
  • AMS: 14N35    Gromov-Witten invariants, quantum cohomology
  • AMS: 14N99    None of the above, but in this section
• AMS: 14Pxx    Real algebraic and real analytic geometry
  AMS: 14P*     (including sub-levels)
  • AMS: 14P10    Semialgebraic sets and related spaces
  • AMS: 14P15    Real analytic and semianalytic sets
  • AMS: 14P20    Nash functions and manifolds
  • AMS: 14P99    None of the above, but in this section
• AMS: 14Qxx    Computational aspects in algebraic geometry
  AMS: 14Q*     (including sub-levels)
  • AMS: 14Q05    Curves
  • AMS: 14Q15    Higher-dimensional varieties
  • AMS: 14Q20    Effectivity
  • AMS: 14Q99    None of the above, but in this section
• AMS: 14Rxx    Affine geometry
  AMS: 14R*     (including sub-levels)
  • AMS: 14R20    Group actions on affine varieties
• AMS: 14Txx    Tropical geometry
  AMS: 14T*     (including sub-levels)

LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY

AMS: 15       All of this section
AMS: 15-XX    Not classified at a more specific level

• AMS: 15-00    General reference works
• AMS: 15-01    Instructional exposition
• AMS: 15-02    Research exposition
• AMS: 15-03    Historical
• AMS: 15-04    Explicit machine computation and programs
• AMS: 15-06    Proceedings, conferences, collections, etc.

• AMS: 15Axx    Basic linear algebra
  AMS: 15A*     (including sub-levels)
  • AMS: 15A03    Vector spaces, linear dependence, rank
  • AMS: 15A04    Linear transformations, semilinear transformations
  • AMS: 15A06    Linear equations
  • AMS: 15A09    Matrix inversion, generalized inverses
  • AMS: 15A12    Conditioning of matrices
  • AMS: 15A15    Determinants, permanents, other special matrix functions
  • AMS: 15A18    Eigenvalues, singular values, and eigenvectors
  • AMS: 15A21    Canonical forms, reductions, classification
  • AMS: 15A22    Matrix pencils
  • AMS: 15A23    Factorization of matrices
  • AMS: 15A24    Matrix equations and identities
  • AMS: 15A27    Commutativity
  • AMS: 15A29    Inverse problems
  • AMS: 15A30    Algebraic systems of matrices
  • AMS: 15A39    Linear inequalities
  • AMS: 15A45    Miscellaneous inequalities involving matrices
  • AMS: 15A60    Norms of matrices, numerical range, applications of functional analysis to matrix theory
  • AMS: 15A63    Quadratic and bilinear forms, inner products
  • AMS: 15A66    Clifford algebras, spinors
  • AMS: 15A69    Multilinear algebra, tensor products
  • AMS: 15A72    Vector and tensor algebra, theory of invariants
  • AMS: 15A75    Exterior algebra, Grassmann algebras
  • AMS: 15A99    Miscellaneous topics
• AMS: 15Bxx    Special matrices
  AMS: 15B*     (including sub-levels)

ASSOCIATIVE RINGS AND ALGEBRAS

AMS: 16       All of this section
AMS: 16-XX    Not classified at a more specific level

• AMS: 16-00    General reference works
• AMS: 16-01    Instructional exposition
• AMS: 16-02    Research exposition
• AMS: 16-06    Proceedings, conferences, collections, etc.

• AMS: 16Bxx    General and miscellaneous
  AMS: 16B*     (including sub-levels)
  • AMS: 16B50    Category-theoretic methods and results (except as in 16D90)
• AMS: 16Dxx    Modules, bimodules and ideals
  AMS: 16D*     (including sub-levels)
  • AMS: 16D10    General module theory
  • AMS: 16D20    Bimodules
  • AMS: 16D25    Ideals
  • AMS: 16D30    Infinite-dimensional simple rings (except as in 16Kxx)
  • AMS: 16D40    Free, projective, and flat modules and ideals
  • AMS: 16D50    Injective modules, self-injective rings
  • AMS: 16D60    Simple and semisimple modules, primitive rings and ideals
  • AMS: 16D70    Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
  • AMS: 16D90    Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
• AMS: 16Exx    Homological methods
  AMS: 16E*     (including sub-levels)
  • AMS: 16E05    Syzygies, resolutions, complexes
  • AMS: 16E10    Homological dimension
  • AMS: 16E20    Grothendieck groups, $K$-theory, etc.
  • AMS: 16E30    Homological functors on modules (Tor, Ext, etc.)
  • AMS: 16E40    (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
  • AMS: 16E45    Differential graded algebras and applications
  • AMS: 16E50    von Neumann regular rings and generalizations
  • AMS: 16E99    None of the above, but in this section
• AMS: 16Gxx    Representation theory of rings and algebras
  AMS: 16G*     (including sub-levels)
  • AMS: 16G10    Representations of Artinian rings
  • AMS: 16G20    Representations of quivers and partially ordered sets
  • AMS: 16G30    Representations of orders, lattices, algebras over commutative rings
  • AMS: 16G50    Cohen-Macaulay modules
  • AMS: 16G60    Representation type (finite, tame, wild, etc.)
  • AMS: 16G70    Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
  • AMS: 16G99    None of the above, but in this section
• AMS: 16Hxx    Algebras and orders
  AMS: 16H*     (including sub-levels)
• AMS: 16Kxx    Division rings and semisimple Artin rings
  AMS: 16K*     (including sub-levels)
  • AMS: 16K20    Finite-dimensional
• AMS: 16Lxx    Local rings and generalizations
  AMS: 16L*     (including sub-levels)
  • AMS: 16L60    Quasi-Frobenius rings
• AMS: 16Nxx    Radicals and radical properties of rings
  AMS: 16N*     (including sub-levels)
  • AMS: 16N40    Nil and nilpotent radicals, sets, ideals, rings
  • AMS: 16N60    Prime and semiprime rings
• AMS: 16Pxx    Chain conditions, growth conditions, and other forms of finiteness
  AMS: 16P*     (including sub-levels)
  • AMS: 16P10    Finite rings and finite-dimensional algebras
  • AMS: 16P20    Artinian rings and modules
  • AMS: 16P40    Noetherian rings and modules
  • AMS: 16P50    Localization and Noetherian rings
  • AMS: 16P60    Chain conditions on annihilators and summands: Goldie-type conditions , Krull dimension
• AMS: 16Rxx    Rings with polynomial identity
  AMS: 16R*     (including sub-levels)
  • AMS: 16R10    $T$-ideals, identities, varieties of rings and algebras
• AMS: 16Sxx    Rings and algebras arising under various constructions
  AMS: 16S*     (including sub-levels)
  • AMS: 16S10    Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
  • AMS: 16S15    Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
  • AMS: 16S30    Universal enveloping algebras of Lie algebras
  • AMS: 16S32    Rings of differential operators
  • AMS: 16S34    Group rings , Laurent polynomial rings
  • AMS: 16S35    Twisted and skew group rings, crossed products
  • AMS: 16S36    Ordinary and skew polynomial rings and semigroup rings
  • AMS: 16S37    Quadratic and Koszul algebras
  • AMS: 16S40    Smash products of general Hopf actions
  • AMS: 16S50    Endomorphism rings; matrix rings
  • AMS: 16S80    Deformations of rings
  • AMS: 16S90    Maximal ring of quotients, torsion theories, radicals on module categories
  • AMS: 16S99    None of the above, but in this section
• AMS: 16Txx    Hopf algebras, quantum groups and related topics
  AMS: 16T*     (including sub-levels)
  • AMS: 16T05    Hopf algebras and their applications
• AMS: 16Uxx    Conditions on elements
  AMS: 16U*     (including sub-levels)
  • AMS: 16U10    Integral domains
  • AMS: 16U60    Units, groups of units
• AMS: 16Wxx    Rings and algebras with additional structure
  AMS: 16W*     (including sub-levels)
  • AMS: 16W10    Rings with involution; Lie, Jordan and other nonassociative structures
  • AMS: 16W20    Automorphisms and endomorphisms
  • AMS: 16W25    Derivations, actions of Lie algebras
  • AMS: 16W50    Graded rings and modules
  • AMS: 16W55    ``Super'' (or ``skew'') structure
  • AMS: 16W60    Valuations, completions, formal power series and related constructions
• AMS: 16Yxx    Generalizations
  AMS: 16Y*     (including sub-levels)
  • AMS: 16Y60    Semirings
• AMS: 16Zxx    Computational aspects of associative rings
  AMS: 16Z*     (including sub-levels)
  • AMS: 16Z05    Computational aspects of associative rings

NONASSOCIATIVE RINGS AND ALGEBRAS

AMS: 17       All of this section
AMS: 17-XX    Not classified at a more specific level

• AMS: 17-01    Instructional exposition
• AMS: 17-02    Research exposition
• AMS: 17-04    Explicit machine computation and programs
• AMS: 17-06    Proceedings, conferences, collections, etc.

• AMS: 17Axx    General nonassociative rings
  AMS: 17A*     (including sub-levels)
  • AMS: 17A01    General theory
  • AMS: 17A30    Algebras satisfying other identities
  • AMS: 17A35    Division algebras
  • AMS: 17A40    Ternary compositions
  • AMS: 17A70    Superalgebras
  • AMS: 17A75    Composition algebras
• AMS: 17Bxx    Lie algebras and Lie superalgebras
  AMS: 17B*     (including sub-levels)
  • AMS: 17B05    Structure theory
  • AMS: 17B10    Representations, algebraic theory (weights)
  • AMS: 17B15    Representations, analytic theory
  • AMS: 17B20    Simple, semisimple, reductive (super)algebras (roots)
  • AMS: 17B25    Exceptional (super)algebras
  • AMS: 17B30    Solvable, nilpotent (super)algebras
  • AMS: 17B35    Universal enveloping algebras
  • AMS: 17B37    Quantum groups (quantized enveloping algebras) and related deformations
  • AMS: 17B40    Automorphisms, derivations, other operators
  • AMS: 17B45    Lie algebras of linear algebraic groups
  • AMS: 17B50    Modular Lie (super)algebras
  • AMS: 17B55    Homological methods in Lie (super)algebras
  • AMS: 17B56    Cohomology of Lie (super)algebras
  • AMS: 17B60    Lie (super)algebras associated with other structures (associative, Jordan, etc.)
  • AMS: 17B63    Poisson algebras
  • AMS: 17B65    Infinite-dimensional Lie (super)algebras
  • AMS: 17B67    Kac-Moody algebras (structure and representation theory)
  • AMS: 17B68    Virasoro and related algebras
  • AMS: 17B69    Vertex operators; vertex operator algebras and related structures
  • AMS: 17B80    Applications to integrable systems
  • AMS: 17B81    Applications to physics
  • AMS: 17B99    None of the above, but in this section
• AMS: 17Cxx    Jordan algebras (algebras, triples and pairs)
  AMS: 17C*     (including sub-levels)
  • AMS: 17C10    Structure theory
  • AMS: 17C20    Simple, semisimple algebras
  • AMS: 17C30    Associated groups, automorphisms
  • AMS: 17C40    Exceptional Jordan structures
  • AMS: 17C65    Jordan structures on Banach spaces and algebras
• AMS: 17Dxx    Other nonassociative rings and algebras
  AMS: 17D*     (including sub-levels)
  • AMS: 17D05    Alternative rings

CATEGORY THEORY; HOMOLOGICAL ALGEBRA

AMS: 18       All of this section
AMS: 18-XX    Not classified at a more specific level

• AMS: 18-00    General reference works
• AMS: 18-01    Instructional exposition
• AMS: 18-02    Research exposition
• AMS: 18-06    Proceedings, conferences, collections, etc.

• AMS: 18Axx    General theory of categories and functors
  AMS: 18A*     (including sub-levels)
  • AMS: 18A05    Definitions, generalizations
  • AMS: 18A15    Foundations, relations to logic and deductive systems
  • AMS: 18A25    Functor categories, comma categories
  • AMS: 18A35    Categories admitting limits (complete categories), functors preserving limits, completions
  • AMS: 18A40    Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
  • AMS: 18A99    None of the above, but in this section
• AMS: 18Bxx    Special categories
  AMS: 18B*     (including sub-levels)
  • AMS: 18B05    Category of sets, characterizations
  • AMS: 18B15    Embedding theorems, universal categories
  • AMS: 18B20    Categories of machines, automata, operative categories
  • AMS: 18B25    Topoi
  • AMS: 18B30    Categories of topological spaces and continuous mappings
  • AMS: 18B40    Groupoids, semigroupoids, semigroups, groups (viewed as categories)
  • AMS: 18B99    None of the above, but in this section
• AMS: 18Cxx    Categories and theories
  AMS: 18C*     (including sub-levels)
  • AMS: 18C10    Theories (e.g. algebraic theories), structure, and semantics
  • AMS: 18C15    Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
• AMS: 18Dxx    Categories with structure
  AMS: 18D*     (including sub-levels)
  • AMS: 18D05    Double categories, $2$-categories, bicategories and generalizations
  • AMS: 18D10    Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
  • AMS: 18D15    Closed categories (closed monoidal and Cartesian closed categories, etc.)
  • AMS: 18D20    Enriched categories (over closed or monoidal categories)
  • AMS: 18D30    Fibered categories
  • AMS: 18D35    Structured objects in a category (group objects, etc.)
  • AMS: 18D50    Operads
  • AMS: 18D99    None of the above, but in this section
• AMS: 18Exx    Abelian categories
  AMS: 18E*     (including sub-levels)
  • AMS: 18E05    Preadditive, additive categories
  • AMS: 18E10    Exact categories, abelian categories
  • AMS: 18E20    Embedding theorems
  • AMS: 18E30    Derived categories, triangulated categories
  • AMS: 18E35    Localization of categories
  • AMS: 18E99    None of the above, but in this section
• AMS: 18Fxx    Categories and geometry
  AMS: 18F*     (including sub-levels)
  • AMS: 18F05    Local categories and functors
  • AMS: 18F10    Grothendieck topologies
  • AMS: 18F15    Abstract manifolds and fiber bundles
  • AMS: 18F20    Presheaves and sheaves
  • AMS: 18F25    Algebraic $K$-theory and $L$-theory
  • AMS: 18F30    Grothendieck groups
  • AMS: 18F99    None of the above, but in this section
• AMS: 18Gxx    Homological algebra
  AMS: 18G*     (including sub-levels)
  • AMS: 18G05    Projectives and injectives
  • AMS: 18G10    Resolutions; derived functors
  • AMS: 18G15    Ext and Tor, generalizations, Künneth formula
  • AMS: 18G20    Homological dimension
  • AMS: 18G30    Simplicial sets, simplicial objects (in a category)
  • AMS: 18G40    Spectral sequences, hypercohomology
  • AMS: 18G50    Nonabelian homological algebra
  • AMS: 18G55    Homotopical algebra
  • AMS: 18G60    Other (co)homology theories

$K$-THEORY

AMS: 19       All of this section
AMS: 19-XX    Not classified at a more specific level

• AMS: 19-00    General reference works
• AMS: 19-01    Instructional exposition
• AMS: 19-02    Research exposition
• AMS: 19-03    Historical
• AMS: 19-06    Proceedings, conferences, collections, etc.

• AMS: 19Axx    Grothendieck groups and $K_0$
  AMS: 19A*     (including sub-levels)
  • AMS: 19A22    Frobenius induction, Burnside and representation rings
  • AMS: 19A31    $K_0$ of group rings and orders
  • AMS: 19A49    $K_0$ of other rings
• AMS: 19Bxx    Whitehead groups and $K_1$
  AMS: 19B*     (including sub-levels)
  • AMS: 19B37    Congruence subgroup problems
• AMS: 19Cxx    Steinberg groups and $K_2$
  AMS: 19C*     (including sub-levels)
  • AMS: 19C09    Central extensions and Schur multipliers
• AMS: 19Dxx    Higher algebraic $K$-theory
  AMS: 19D*     (including sub-levels)
  • AMS: 19D23    Symmetric monoidal categories
  • AMS: 19D25    Karoubi-Villamayor-Gersten $K$-theory
  • AMS: 19D45    Higher symbols, Milnor $K$-theory
  • AMS: 19D50    Computations of higher $K$-theory of rings
  • AMS: 19D55    $K$-theory and homology; cyclic homology and cohomology
  • AMS: 19D99    None of the above, but in this section
• AMS: 19Exx    $K$-theory in geometry
  AMS: 19E*     (including sub-levels)
  • AMS: 19E08    $K$-theory of schemes
  • AMS: 19E15    Algebraic cycles and motivic cohomology
• AMS: 19Fxx    $K$-theory in number theory
  AMS: 19F*     (including sub-levels)
  • AMS: 19F05    Generalized class field theory
  • AMS: 19F27    Étale cohomology, higher regulators, zeta and $L$-functions
• AMS: 19Gxx    $K$-theory of forms
  AMS: 19G*     (including sub-levels)
  • AMS: 19G12    Witt groups of rings
  • AMS: 19G24    $L$-theory of group rings
• AMS: 19Jxx    Obstructions from topology
  AMS: 19J*     (including sub-levels)
  • AMS: 19J25    Surgery obstructions
• AMS: 19Kxx    $K$-theory and operator algebras
  AMS: 19K*     (including sub-levels)
  • AMS: 19K14    $K_0$ as an ordered group, traces
  • AMS: 19K35    Kasparov theory ($KK$-theory)
  • AMS: 19K56    Index theory
  • AMS: 19K99    None of the above, but in this section
• AMS: 19Lxx    Topological $K$-theory
  AMS: 19L*     (including sub-levels)
  • AMS: 19L10    Riemann-Roch theorems, Chern characters
  • AMS: 19L20    $J$-homomorphism, Adams operations
  • AMS: 19L41    Connective $K$-theory, cobordism
  • AMS: 19L47    Equivariant $K$-theory
  • AMS: 19L64    Computations, geometric applications
• AMS: 19Mxx    Miscellaneous applications of $K$$K$-theory
  AMS: 19M*     (including sub-levels)
  • AMS: 19M05    Miscellaneous applications of $K$-theory

GROUP THEORY AND GENERALIZATIONS

AMS: 20       All of this section
AMS: 20-XX    Not classified at a more specific level

• AMS: 20-01    Instructional exposition
• AMS: 20-02    Research exposition
• AMS: 20-03    Historical
• AMS: 20-04    Explicit machine computation and programs
• AMS: 20-06    Proceedings, conferences, collections, etc.

• AMS: 20Axx    Foundations
  AMS: 20A*     (including sub-levels)
  • AMS: 20A15    Applications of logic to group theory
• AMS: 20Bxx    Permutation groups
  AMS: 20B*     (including sub-levels)
  • AMS: 20B05    General theory for finite groups
  • AMS: 20B07    General theory for infinite groups
  • AMS: 20B15    Primitive groups
  • AMS: 20B22    Multiply transitive infinite groups
  • AMS: 20B25    Finite automorphism groups of algebraic, geometric, or combinatorial structures
  • AMS: 20B27    Infinite automorphism groups
  • AMS: 20B30    Symmetric groups
  • AMS: 20B35    Subgroups of symmetric groups
  • AMS: 20B40    Computational methods
• AMS: 20Cxx    Representation theory of groups
  AMS: 20C*     (including sub-levels)
  • AMS: 20C05    Group rings of finite groups and their modules
  • AMS: 20C07    Group rings of infinite groups and their modules
  • AMS: 20C08    Hecke algebras and their representations
  • AMS: 20C10    Integral representations of finite groups
  • AMS: 20C11    $p$-adic representations of finite groups
  • AMS: 20C15    Ordinary representations and characters
  • AMS: 20C20    Modular representations and characters
  • AMS: 20C25    Projective representations and multipliers
  • AMS: 20C30    Representations of finite symmetric groups
  • AMS: 20C33    Representations of finite groups of Lie type
  • AMS: 20C35    Applications of group representations to physics
  • AMS: 20C40    Computational methods
• AMS: 20Dxx    Abstract finite groups
  AMS: 20D*     (including sub-levels)
  • AMS: 20D05    Classification of simple and nonsolvable groups
  • AMS: 20D06    Simple groups: alternating groups and groups of Lie type
  • AMS: 20D08    Simple groups: sporadic groups
  • AMS: 20D15    Nilpotent groups, $p$-groups
  • AMS: 20D20    Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
  • AMS: 20D25    Special subgroups (Frattini, Fitting, etc.)
  • AMS: 20D30    Series and lattices of subgroups
  • AMS: 20D35    Subnormal subgroups
  • AMS: 20D40    Products of subgroups
• AMS: 20Exx    Structure and classification of infinite or finite groups
  AMS: 20E*     (including sub-levels)
  • AMS: 20E05    Free nonabelian groups
  • AMS: 20E06    Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
  • AMS: 20E07    Subgroup theorems; subgroup growth
  • AMS: 20E08    Groups acting on trees
  • AMS: 20E10    Quasivarieties and varieties of groups
  • AMS: 20E15    Chains and lattices of subgroups, subnormal subgroups
  • AMS: 20E18    Limits, profinite groups
  • AMS: 20E22    Extensions, wreath products, and other compositions
  • AMS: 20E26    Residual properties and generalizations
  • AMS: 20E28    Maximal subgroups
  • AMS: 20E32    Simple groups
  • AMS: 20E34    General structure theorems
  • AMS: 20E42    Groups with a $BN$-pair; buildings
• AMS: 20Fxx    Special aspects of infinite or finite groups
  AMS: 20F*     (including sub-levels)
  • AMS: 20F05    Generators, relations, and presentations
  • AMS: 20F06    Cancellation theory; application of van Kampen diagrams
  • AMS: 20F10    Word problems, other decision problems, connections with logic and automata
  • AMS: 20F12    Commutator calculus
  • AMS: 20F14    Derived series, central series, and generalizations
  • AMS: 20F16    Solvable groups, supersolvable groups
  • AMS: 20F18    Nilpotent groups
  • AMS: 20F28    Automorphism groups of groups
  • AMS: 20F29    Representations of groups as automorphism groups of algebraic systems
  • AMS: 20F34    Fundamental groups and their automorphisms
  • AMS: 20F36    Braid groups; Artin groups
  • AMS: 20F38    Other groups related to topology or analysis
  • AMS: 20F40    Associated Lie structures
  • AMS: 20F50    Periodic groups; locally finite groups
  • AMS: 20F55    Reflection and Coxeter groups
  • AMS: 20F60    Ordered groups
  • AMS: 20F65    Geometric group theory
  • AMS: 20F67    Hyperbolic groups and nonpositively curved groups
• AMS: 20Gxx    Linear algebraic groups (classical groups)
  AMS: 20G*     (including sub-levels)
  • AMS: 20G05    Representation theory
  • AMS: 20G10    Cohomology theory
  • AMS: 20G15    Linear algebraic groups over arbitrary fields
  • AMS: 20G20    Linear algebraic groups over the reals, the complexes, the quaternions
  • AMS: 20G25    Linear algebraic groups over local fields and their integers
  • AMS: 20G30    Linear algebraic groups over global fields and their integers
  • AMS: 20G35    Linear algebraic groups over adèles and other rings and schemes
  • AMS: 20G40    Linear algebraic groups over finite fields
  • AMS: 20G42    Quantum groups (quantized function algebras) and their representations
  • AMS: 20G44    Kac-Moody groups
  • AMS: 20G45    Applications to physics
  • AMS: 20G99    None of the above, but in this section
• AMS: 20Hxx    Other groups of matrices
  AMS: 20H*     (including sub-levels)
  • AMS: 20H05    Unimodular groups, congruence subgroups
  • AMS: 20H10    Fuchsian groups and their generalizations
  • AMS: 20H15    Other geometric groups, including crystallographic groups
  • AMS: 20h20    Other matrix groups over fields
  • AMS: 20h20    Other matrix groups over finite fields
• AMS: 20Jxx    Connections with homological algebra and category theory
  AMS: 20J*     (including sub-levels)
  • AMS: 20J05    Homological methods in group theory
  • AMS: 20J06    Cohomology of groups
  • AMS: 20J15    Category of groups
• AMS: 20Kxx    Abelian groups
  AMS: 20K*     (including sub-levels)
• AMS: 20Lxx    Groupoids (i.e. small categories in which all morphisms are isomorphisms)
  AMS: 20L*     (including sub-levels)
• AMS: 20Mxx    Semigroups
  AMS: 20M*     (including sub-levels)
  • AMS: 20M05    Free semigroups, generators and relations, word problems
  • AMS: 20M07    Varieties of semigroups
  • AMS: 20M10    General structure theory
  • AMS: 20M17    Regular semigroups
  • AMS: 20M20    Semigroups of transformations, etc.
  • AMS: 20M30    Representation of semigroups; actions of semigroups on sets
  • AMS: 20M35    Semigroups in automata theory, linguistics, etc.
  • AMS: 20M50    Connections of semigroups with homological algebra and category theory
• AMS: 20Nxx    Other generalizations of groups
  AMS: 20N*     (including sub-levels)
  • AMS: 20N20    Hypergroups
• AMS: 20Pxx    Probabilistic methods in group theory
  AMS: 20P*     (including sub-levels)
  • AMS: 20P05    Probabilistic methods in group theory

TOPOLOGICAL GROUPS, LIE GROUPS

AMS: 22       All of this section
AMS: 22-XX    Not classified at a more specific level

• AMS: 22-01    Instructional exposition
• AMS: 22-02    Research exposition
• AMS: 22-03    Historical
• AMS: 22-06    Proceedings, conferences, collections, etc.

• AMS: 22Axx    Topological and differentiable algebraic systems
  AMS: 22A*     (including sub-levels)
  • AMS: 22A10    Analysis on general topological groups
  • AMS: 22A22    Topological groupoids (including differentiable and Lie groupoids)
  • AMS: 22A25    Representations of general topological groups and semigroups
  • AMS: 22A26    Topological semilattices, lattices and applications
• AMS: 22Bxx    Locally compact abelian groups (LCA groups)
  AMS: 22B*     (including sub-levels)
  • AMS: 22B10    Structure of group algebras of LCA groups
  • AMS: 22B99    None of the above, but in this section
• AMS: 22Cxx    Compact groups
  AMS: 22C*     (including sub-levels)
  • AMS: 22C05    Compact groups
• AMS: 22Dxx    Locally compact groups and their algebras
  AMS: 22D*     (including sub-levels)
  • AMS: 22D05    General properties and structure of locally compact groups
  • AMS: 22D10    Unitary representations of locally compact groups
  • AMS: 22D25    $C^*$-algebras and $W$*-algebras in relation to group representations
  • AMS: 22D30    Induced representations
  • AMS: 22D35    Duality theorems
  • AMS: 22D40    Ergodic theory on groups
• AMS: 22Exx    Lie groups
  AMS: 22E*     (including sub-levels)
  • AMS: 22E05    Local Lie groups
  • AMS: 22E10    General properties and structure of complex Lie groups
  • AMS: 22E15    General properties and structure of real Lie groups
  • AMS: 22E20    General properties and structure of other Lie groups
  • AMS: 22E25    Nilpotent and solvable Lie groups
  • AMS: 22E27    Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
  • AMS: 22E30    Analysis on real and complex Lie groups
  • AMS: 22E35    Analysis on $p$-adic Lie groups
  • AMS: 22E40    Discrete subgroups of Lie groups
  • AMS: 22E41    Continuous cohomology
  • AMS: 22E45    Representations of Lie and linear algebraic groups over real fields: analytic methods
  • AMS: 22E46    Semisimple Lie groups and their representations
  • AMS: 22E47    Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
  • AMS: 22E50    Representations of Lie and linear algebraic groups over local fields
  • AMS: 22E55    Representations of Lie and linear algebraic groups over global fields and adèle rings
  • AMS: 22E60    Lie algebras of Lie groups
  • AMS: 22E65    Infinite-dimensional Lie groups and their Lie algebras
  • AMS: 22E67    Loop groups and related constructions, group-theoretic treatment
  • AMS: 22E70    Applications of Lie groups to physics; explicit representations
  • AMS: 22E99    None of the above, but in this section
• AMS: 22Fxx    Noncompact transformation groups
  AMS: 22F*     (including sub-levels)

Letzte Änderung: 20.07.2012 Gabriele Dörflinger