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 637
13-03 History of commutative algebra [Consider also classification numbers pertaining to Section 01-XX] 157
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 1068
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure [See also 13B22] 886
13A70 General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) [See also 05C25, 05E40] 41
13B22 Integral closure of commutative rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 871
13B40 Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25] 153
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} 8208
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 1004
13D10 Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 14D15, 32Gxx] 329
13D15 Grothendieck groups, \(K\)-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50] 628
13F15 Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05] 789
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes [See also 55U10] 879
13Pxx Computational aspects and applications of commutative rings [See also 14Qxx, 68W30] {For software etc., see 13-04} 4842
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 362