| 13-XX |
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Commutative algebra |
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13-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to commutative algebra |
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13-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra |
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13-02 |
Research exposition (monographs, survey articles) pertaining to commutative algebra |
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13-03 |
History of commutative algebra [Consider also classification numbers from Section 01-XX] |
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13-04 |
Software, source code, etc. for problems pertaining to commutative algebra |
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13-06 |
Proceedings, conferences, collections, etc. pertaining to commutative algebra |
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13A02 |
Graded rings [See also 16W50] |
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13A05 |
Divisibility and factorizations in commutative rings [See also 13F15] |
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13A15 |
Ideals and multiplicative ideal theory in commutative rings |
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13A18 |
Valuations and their generalizations for commutative rings [See also 12J20] |
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13A30 |
Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics |
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13A35 |
Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure [See also 13B22] |
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13A50 |
Actions of groups on commutative rings; invariant theory [See also 14L24] |
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13A99 |
None of the above, but in this section |
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13B02 |
Extension theory of commutative rings |
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13B05 |
Galois theory and commutative ring extensions |
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13B10 |
Morphisms of commutative rings |
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13B21 |
Integral dependence in commutative rings; going up, going down |
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13B22 |
Integral closure of commutative rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) |
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13B25 |
Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] |
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13B30 |
Rings of fractions and localization for commutative rings [See also 16S85] |
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13B35 |
Completion of commutative rings [See also 13J10] |
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13B40 |
Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25] |
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13B99 |
None of the above, but in this section |
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13C05 |
Structure, classification theorems for modules and ideals in commutative rings |
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13C10 |
Projective and free modules and ideals in commutative rings [See also 19A13] |
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13C11 |
Injective and flat modules and ideals in commutative rings |
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13C12 |
Torsion modules and ideals in commutative rings |
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13C13 |
Other special types of modules and ideals in commutative rings |
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13C14 |
Cohen-Macaulay modules [See also 13H10] |
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13C15 |
Dimension theory, depth, related commutative rings (catenary, etc.) |
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13C20 |
Class groups [See also 11R29] |
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13C40 |
Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] |
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13C60 |
Module categories and commutative rings |
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13C99 |
None of the above, but in this section |
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13D02 |
Syzygies, resolutions, complexes and commutative rings |
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13D03 |
(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) |
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13D05 |
Homological dimension and commutative rings |
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13D07 |
Homological functors on modules of commutative rings (Tor, Ext, etc.) |
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13D09 |
Derived categories and commutative rings |
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13D10 |
Deformations and infinitesimal methods in commutative ring theory [See also 14B10, 14B12, 14D15, 32Gxx] |
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13D15 |
Grothendieck groups, $K$-theory and commutative rings [See also 14C35, 18F30, 19Axx, 19D50] |
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13D22 |
Homological conjectures (intersection theorems) in commutative ring theory |
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13D30 |
Torsion theory for commutative rings [See also 13C12, 18E40] |
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13D40 |
Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
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13D45 |
Local cohomology and commutative rings [See also 14B15] |
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13D99 |
None of the above, but in this section |
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13E05 |
Commutative Noetherian rings and modules |
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13E10 |
Commutative Artinian rings and modules, finite-dimensional algebras |
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13E15 |
Commutative rings and modules of finite generation or presentation; number of generators |
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13E99 |
None of the above, but in this section |
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13F05 |
Dedekind, Prüfer, Krull and Mori rings and their generalizations |
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13F07 |
Euclidean rings and generalizations |
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13F10 |
Principal ideal rings |
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13F15 |
Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05] |
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13F20 |
Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] |
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13F25 |
Formal power series rings [See also 13J05] |
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13F30 |
Valuation rings [See also 13A18] |
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13F35 |
Witt vectors and related rings |
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13F40 |
Excellent rings |
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13F45 |
Seminormal rings |
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13F50 |
Rings with straightening laws, Hodge algebras |
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13F55 |
Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes [See also 55U10] |
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13F60 |
Cluster algebras |
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13F99 |
None of the above, but in this section |
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13G05 |
Integral domains |
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13G99 |
None of the above, but in this section |
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13H05 |
Regular local rings |
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13H10 |
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] |
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13H15 |
Multiplicity theory and related topics [See also 14C17] |
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13H99 |
None of the above, but in this section |
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13J05 |
Power series rings [See also 13F25] |
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13J07 |
Analytical algebras and rings [See also 32B05] |
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13J10 |
Complete rings, completion [See also 13B35] |
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13J15 |
Henselian rings [See also 13B40] |
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13J20 |
Global topological rings |
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13J25 |
Ordered rings [See also 06F25] |
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13J30 |
Real algebra [See also 12D15, 14Pxx] |
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13J99 |
None of the above, but in this section |
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13L05 |
Applications of logic to commutative algebra [See also 03Cxx, 03Hxx] |
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13L99 |
None of the above, but in this section |
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13M05 |
Structure of finite commutative rings |
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13M10 |
Polynomials and finite commutative rings |
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13M99 |
None of the above, but in this section |
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13N05 |
Modules of differentials |
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13N10 |
Commutative rings of differential operators and their modules [See also 16S32, 32C38] |
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13N15 |
Derivations and commutative rings |
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13N99 |
None of the above, but in this section |
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13P05 |
Polynomials, factorization in commutative rings [See also 12-08] |
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13P10 |
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
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13P15 |
Solving polynomial systems; resultants |
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13P20 |
Computational homological algebra [See also 13Dxx] |
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13P25 |
Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) |
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13P99 |
None of the above, but in this section |
