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**►****Foundations****▼****Algebra****▼****11-XX Number theory****►****11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****11Axx Elementary number theory****►****11Bxx Sequences and sets****►****11Cxx Polynomials and matrices****►****11Dxx Diophantine equations****▼****11Exx Forms and linear algebraic groups**- 11E04 Quadratic forms over general fields
- 11E08 Quadratic forms over local rings and fields
- 11E10 Forms over real fields
- 11E12 Quadratic forms over global rings and fields
- 11E16 General binary quadratic forms
- 11E20 General ternary and quaternary quadratic forms; forms of more than two variables
- 11E25 Sums of squares and representations by other particular quadratic forms
- 11E39 Bilinear and Hermitian forms
- 11E41 Class numbers of quadratic and Hermitian forms
- 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
- 11E57 Classical groups
- 11E70
*K*-theory of quadratic and Hermitian forms - 11E72 Galois cohomology of linear algebraic groups
- 11E76 Forms of degree higher than two
- 11E81 Algebraic theory of quadratic forms; Witt groups and rings
- 11E88 Quadratic spaces; Clifford algebras
- 11E95
*p*-adic theory - 11E99 None of the above, but in this section

**►****11Fxx Discontinuous groups and automorphic forms****►****11Gxx Arithmetic algebraic geometry (Diophantine geometry)****►****11Hxx Geometry of numbers****►****11Jxx Diophantine approximation, transcendental number theory****▼****11Kxx Probabilistic theory: distribution modulo***1*; metric theory of algorithms- 11K06 General theory of distribution modulo
*1* - 11K16 Normal numbers, radix expansions, etc.
- 11K31 Special sequences
- 11K36 Well-distributed sequences and other variations
- 11K38 Irregularities of distribution, discrepancy
- 11K41 Continuous,
*p*-adic and abstract analogues - 11K45 Pseudo-random numbers; Monte Carlo methods
- 11K50 Metric theory of continued fractions
- 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
- 11K60 Diophantine approximation
- 11K65 Arithmetic functions
- 11K70 Harmonic analysis and almost periodicity
- 11K99 None of the above, but in this section

- 11K06 General theory of distribution modulo
**►****11Lxx Exponential sums and character sums****►****11Mxx Zeta and***L*-functions: analytic theory**►****11Nxx Multiplicative number theory****►****11Pxx Additive number theory; partitions****►****11Rxx Algebraic number theory: global fields****►****11Sxx Algebraic number theory: local and***p*-adic fields**►****11Txx Finite fields and commutative rings (number-theoretic aspects)****▼****11Uxx Connections with logic****►****11Yxx Computational number theory**- 11Zxx Miscellaneous applications of number theory

**►****12-XX Field theory and polynomials****►****13-XX Commutative rings and algebras****►****14-XX Algebraic geometry****►****15-XX Linear and multilinear algebra; matrix theory****▼****16-XX Associative rings and algebras****►****16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****16Bxx General and miscellaneous****►****16Dxx Modules, bimodules and ideals****►****16Exx Homological methods****►****16Gxx Representation theory of rings and algebras**- 16H05 Orders and arithmetic, separable algebras, Azumaya algebras
**►****16Kxx Division rings and semisimple Artin rings****►****16Lxx Local rings and generalizations****►****16Nxx Radicals and radical properties of rings****►****16Pxx Chain conditions, growth conditions, and other forms of finiteness****►****16Rxx Rings with polynomial identity****►****16Sxx Rings and algebras arising under various constructions****►****16Uxx Conditions on elements****►****16Wxx Rings and algebras with additional structure****►****16Yxx Generalizations**- 16Z05 Computational aspects of associative rings

**►****17-XX Nonassociative rings and algebras****▼****18-XX Category theory; homological algebra****►****18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****18Axx General theory of categories and functors****►****18Bxx Special categories****►****18Cxx Categories and theories****►****18Dxx Categories with structure****►****18Exx Abelian categories****►****18Fxx Categories and geometry****▼****18Gxx Homological algebra**- 18G05 Projectives and injectives
- 18G10 Resolutions; derived functors
- 18G15 Ext and Tor, generalizations, Künneth formula
- 18G20 Homological dimension
- 18G25 Relative homological algebra, projective classes
- 18G30 Simplicial sets, simplicial objects (in a category)
- 18G35 Chain complexes
- 18G40 Spectral sequences, hypercohomology
- 18G50 Nonabelian homological algebra
- 18G55 Homotopical algebra
- 18G60 Other (co)homology theories
- 18G99 None of the above, but in this section

**►****19-XX***K*-theory**▼****20-XX Group theory and generalizations****►****20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****20Axx Foundations****►****20Bxx Permutation groups****►****20Cxx Representation theory of groups****▼****20Dxx Abstract finite groups**- 20D05 Classification of simple and nonsolvable groups
- 20D06 Simple groups: alternating groups and groups of Lie type
- 20D08 Simple groups: sporadic groups
- 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes,
*π*-length, ranks - 20D15 Nilpotent groups,
*p*-groups - 20D20 Sylow subgroups, Sylow properties,
*π*-groups,*π*-structure - 20D25 Special subgroups (Frattini, Fitting, etc.)
- 20D30 Series and lattices of subgroups
- 20D35 Subnormal subgroups
- 20D40 Products of subgroups
- 20D45 Automorphisms
- 20D60 Arithmetic and combinatorial problems
- 20D99 None of the above, but in this section

**►****20Exx Structure and classification of infinite or finite groups****▼****20Fxx Special aspects of infinite or finite groups**- 20F05 Generators, relations, and presentations
- 20F06 Cancellation theory; application of van Kampen diagrams
- 20F10 Word problems, other decision problems, connections with logic and automata
- 20F12 Commutator calculus
- 20F14 Derived series, central series, and generalizations
- 20F16 Solvable groups, supersolvable groups
- 20F17 Formations of groups, Fitting classes
- 20F18 Nilpotent groups
- 20F19 Generalizations of solvable and nilpotent groups
- 20F22 Other classes of groups defined by subgroup chains
- 20F24 FC-groups and their generalizations
- 20F28 Automorphism groups of groups
- 20F29 Representations of groups as automorphism groups of algebraic systems
- 20F34 Fundamental groups and their automorphisms
- 20F36 Braid groups; Artin groups
- 20F38 Other groups related to topology or analysis
- 20F40 Associated Lie structures
- 20F45 Engel conditions
- 20F50 Periodic groups; locally finite groups
- 20F55 Reflection and Coxeter groups
- 20F60 Ordered groups
- 20F65 Geometric group theory
- 20F67 Hyperbolic groups and nonpositively curved groups
- 20F69 Asymptotic properties of groups
- 20F99 None of the above, but in this section

**▼****20Gxx Linear algebraic groups (classical groups)**- 20G05 Representation theory
- 20G10 Cohomology theory
- 20G15 Linear algebraic groups over arbitrary fields
- 20G20 Linear algebraic groups over the reals, the complexes, the quaternions
- 20G25 Linear algebraic groups over local fields and their integers
- 20G30 Linear algebraic groups over global fields and their integers
- 20G35 Linear algebraic groups over adčles and other rings and schemes
- 20G40 Linear algebraic groups over finite fields
- 20G42 Quantum groups (quantized function algebras) and their representations
- 20G45 Applications to physics
- 20G99 None of the above, but in this section

**►****20Hxx Other groups of matrices****►****20Jxx Connections with homological algebra and category theory****►****20Kxx Abelian groups**- 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
**►****20Mxx Semigroups****►****20Nxx Other generalizations of groups**- 20P05 Probabilistic methods in group theory

**►****Analysis****►****Differential Equations****►****Transformations****►****Geometry****►****Statistics****►****Applied Mathematics****►****Didactics**

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