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 654
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 1113
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure [See also 13B22] 945
13A70 General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) [See also 05C25, 05E40] 126
13B22 Integral closure of commutative rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 908
13B40 Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25] 159
13C70 Theory of modules and ideals in commutative rings described by combinatorial properties [See also 05C25, 05E40] 14
13Dxx Homological methods in commutative ring theory {For noncommutative rings, see 16Exx; for general categories, see 18Gxx} 8660
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 1027
13D10 Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 14D15, 32Gxx] 341
13D15 Grothendieck groups, \(K\)-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50] 634
13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05] 819
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes [See also 55U10] 970
13Pxx Computational aspects and applications of commutative rings [See also 14Qxx, 68W30] {For software etc., see 13-04} 5131
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 404