08-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general algebraic systems 35
08-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems 117
08-03 History of general algebraic systems [Consider also classification numbers pertaining to Section 01-XX] 39
11-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to number theory 56
11-03 History of number theory [Consider also classification numbers pertaining to Section 01-XX] 1830
11Exx Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63} 8591
11Fxx Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} 18571
11F06 Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 992
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 929
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 1961
11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 74
11F70 Representation-theoretic methods; automorphic representations over local and global fields 2951
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 1253
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63] 962
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx] 1046
11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) 820
11M41 Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10} [See also 11E45, 11F66, 11F70, 11F72] 2756
11N64 Other results on the distribution of values or the characterization of arithmetic functions 609
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10] 767
11R54 Other algebras and orders, and their zeta and \(L\)-functions [See also 11S45, 16Hxx, 16Kxx] 159
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) 1763
12-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory 10
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15} 1349
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx] 806
13-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra 12
13-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra 626
13-03 History of commutative algebra [Consider also classification numbers pertaining to Section 01-XX] 155
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 1053
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure [See also 13B22] 863
13A70 General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) [See also 05C25, 05E40] 33
13B22 Integral closure of commutative rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 866
13B40 Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25] 152
13C70 Theory of modules and ideals in commutative rings described by combinatorial properties [See also 05C25, 05E40] 1
13Dxx Homological methods in commutative ring theory {For noncommutative rings, see 16Exx; for general categories, see 18Gxx} 8118
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 998
13D10 Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 14D15, 32Gxx] 328
13D15 Grothendieck groups, \(K\)-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50] 627
13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05] 786
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes [See also 55U10] 858
13Pxx Computational aspects and applications of commutative rings [See also 14Qxx, 68W30] {For software etc., see 13-04} 4737
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 353
14Qxx Computational aspects in algebraic geometry {For software etc., see 14-04} [See also 12-08, 13Pxx, 68W30] 2561
14Q25 Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx] 1
16-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to associative rings and algebras 30
16-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras 307
16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras 661
16-03 History of associative rings and algebras [Consider also classification numbers pertaining to Section 01-XX] 122
16B50 Category-theoretic methods and results in associative algebras (except as in 16D90) [See also 18-XX] 553
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) 3945
16D90 Module categories in associative algebras [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 3348
16Exx Homological methods in associative algebras {For commutative rings, see 13Dxx; for general categories, see 18Gxx} 10320
16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 672
16Hxx Associative algebras and orders {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30} 2298
16Pxx Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras 8320
16P10 Finite rings and finite-dimensional associative algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx} 2832
16P60 Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension (associative rings and algebras) 1813
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) 619
16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 909
16S34 Group rings [See also 20C05, 20C07], Laurent polynomial rings (associative algebraic aspects) 4580
16S90 Torsion theories; radicals on module categories (associative algebraic aspects) [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} 1493
16W10 Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx] 2371
16W55 “Super” (or “skew”) structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66} 369
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras) [See also 13Jxx] 1351
18-XX Category theory; homological algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} 28834
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 1807
32-XX Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see also 46G20, 58B12} 47207
32B25 Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions 84
33-XX Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11-XX; for representation theory, see 22Exx} 39617
33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 57
33-03 History of special functions [Consider also classification numbers pertaining to Section 01-XX] 154
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) 577
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) {For general orthogonal polynomials and functions, see also 42C05} 9710
33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable 707
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) 2776
33D50 Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable 76
33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) 292
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics 676
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) [See also 68W30] 418
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} 127321
46Hxx Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20} 7010
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] 87659
52B55 Computational aspects related to convexity {For computational methods, see 52-08; for computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx} [See also 68Uxx] 1297
65C20 Probabilistic models, generic numerical methods in probability and statistics [See also 60-08, 62-08] 4444
65E05 General theory of numerical methods in complex analysis (potential theory, etc.) [See also 30-08, 31-08, 32-08] 1426
68-XX Computer science {For papers containing software, source code, etc. in a specific mathematical area, see the classification number -04 in that area} 364299
68Wxx Algorithms in computer science {For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx} 49124
68W30 Symbolic computation and algebraic computation [See also 11Yxx, 12-08, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 11404