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**►****Foundations****▼****Algebra****►****11-XX Number theory****▼****12-XX Field theory and polynomials****►****12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****12Dxx Real and complex fields****►****12Exx General field theory****►****12Fxx Field extensions****►****12Gxx Homological methods (field theory)****►****12Hxx Differential and difference algebra****►****12Jxx Topological fields****►****12Kxx Generalizations of fields****►****12Lxx Connections with logic**- 12Y05 Computational aspects of 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****▼****17-XX Nonassociative rings and algebras****►****17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****17Axx General nonassociative rings****▼****17Bxx Lie algebras and Lie superalgebras**- 17B01 Identities, free Lie (super)algebras
- 17B05 Structure theory
- 17B10 Representations, algebraic theory (weights)
- 17B15 Representations, analytic theory
- 17B20 Simple, semisimple, reductive (super)algebras (roots)
- 17B25 Exceptional (super)algebras
- 17B30 Solvable, nilpotent (super)algebras
- 17B35 Universal enveloping (super)algebras
- 17B37 Quantum groups (quantized enveloping algebras) and related deformations
- 17B40 Automorphisms, derivations, other operators
- 17B45 Lie algebras of linear algebraic groups
- 17B50 Modular Lie (super)algebras
- 17B55 Homological methods in Lie (super)algebras
- 17B56 Cohomology of Lie (super)algebras
- 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
- 17B62 Lie bialgebras
- 17B63 Poisson algebras
- 17B65 Infinite-dimensional Lie (super)algebras
- 17B66 Lie algebras of vector fields and related (super) algebras
- 17B67 Kac-Moody (super)algebras (structure and representation theory)
- 17B68 Virasoro and related algebras
- 17B69 Vertex operators; vertex operator algebras and related structures
- 17B70 Graded Lie (super)algebras
- 17B75 Color Lie (super)algebras
- 17B80 Applications to integrable systems
- 17B81 Applications to physics
- 17B99 None of the above, but in this section

**▼****17Cxx Jordan algebras (algebras, triples and pairs)**- 17C05 Identities and free Jordan structures
- 17C10 Structure theory
- 17C17 Radicals
- 17C20 Simple, semisimple algebras
- 17C27 Idempotents, Peirce decompositions
- 17C30 Associated groups, automorphisms
- 17C36 Associated manifolds
- 17C37 Associated geometries
- 17C40 Exceptional Jordan structures
- 17C50 Jordan structures associated with other structures
- 17C55 Finite-dimensional structures
- 17C60 Division algebras
- 17C65 Jordan structures on Banach spaces and algebras
- 17C70 Super structures
- 17C90 Applications to physics
- 17C99 None of the above, but in this section

**▼****17Dxx Other 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**- 18A05 Definitions, generalizations
- 18A10 Graphs, diagram schemes, precategories
- 18A15 Foundations, relations to logic and deductive systems
- 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
- 18A22 Special properties of functors (faithful, full, etc.)
- 18A23 Natural morphisms, dinatural morphisms
- 18A25 Functor categories, comma categories
- 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
- 18A32 Factorization of morphisms, substructures, quotient structures, congruences, amalgams
- 18A35 Categories admitting limits (complete categories), functors preserving limits, completions
- 18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
- 18A99 None of the above, but in this section

**▼****18Bxx Special categories**- 18B05 Category of sets, characterizations
- 18B10 Category of relations, additive relations
- 18B15 Embedding theorems, universal categories
- 18B20 Categories of machines, automata, operative categories
- 18B25 Topoi
- 18B30 Categories of topological spaces and continuous mappings
- 18B35 Preorders, orders and lattices (viewed as categories)
- 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
- 18B99 None of the above, but in this section

**►****18Cxx Categories and theories****►****18Dxx Categories with structure****►****18Exx Abelian categories****►****18Fxx Categories and geometry****►****18Gxx Homological algebra**

**▼****19-XX***K*-theory**►****19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)****►****19Axx Grothendieck groups and***K*_{0}**►****19Bxx Whitehead groups and***K*_{1}**►****19Cxx Steinberg groups and***K*_{2}**►****19Dxx Higher algebraic***K*-theory**►****19Exx***K*-theory in geometry**►****19Fxx***K*-theory in number theory**►****19Gxx***K*-theory of forms**▼****19Jxx Obstructions from topology****►****19Kxx***K*-theory and operator algebras**►****19Lxx Topological***K*-theory- 19M05 Miscellaneous applications of
*K*-theory

**►****20-XX Group theory and generalizations**

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

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