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based on the MSC 2000 classification. You can browse down to the individual notation, the links available will direct you to the appropriate place in the GBV OPAC, which uses a notation related to, but different from MSC. Note: Not all books available are contained in the online catalogue. Please use the Goettingen State University Library's Alphabetical Catalogue to search for monographs, dissertations and journals missing in the OPAC. |

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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****►****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**- 16R10
*T*-ideals, identities, varieties of rings and algebras - 16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
- 16R30 Trace rings and invariant theory
- 16R40 Identities other than those of matrices over commutative rings
- 16R50 Other kinds of identities (generalized polynomial, rational, involution)
- 16R99 None of the above, but in this section

- 16R10
**►****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**- 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**- 18C05 Equational categories
- 18C10 Theories (e.g. algebraic theories), structure, and semantics
- 18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
- 18C20 Algebras and Kleisli categories associated with monads
- 18C30 Sketches and generalizations
- 18C35 Accessible and locally presentable categories
- 18C50 Categorical semantics of formal languages
- 18C99 None of the above, but in this section

**▼****18Dxx Categories with structure**- 18D05 Double categories,
*2*-categories, bicategories and generalizations - 18D10 Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
- 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
- 18D20 Enriched categories (over closed or monoidal categories)
- 18D25 Strong functors, strong adjunctions
- 18D30 Fibered categories
- 18D35 Structured objects in a category (group objects, etc.)
- 18D50 Operads
- 18D99 None of the above, but in this section

- 18D05 Double categories,
**►****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- 19D06
*Q*- and plus-constructions - 19D10 Algebraic
*K*-theory of spaces - 19D23 Symmetric monoidal categories
- 19D25 Karoubi-Villamayor-Gersten
*K*-theory - 19D35 Negative
*K*-theory, NK and Nil - 19D45 Higher symbols, Milnor
*K*-theory - 19D50 Computations of higher
*K*-theory of rings - 19D55
*K*-theory and homology; cyclic homology and cohomology - 19D99 None of the above, but in this section

- 19D06
**▼****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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