| 13-XX | | Prev: 12 | Up: Top | Next: 14 | |
| Commutative rings and algebras [xref: 14A05, 32Bxx] |
13-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.)
| 13-01 |
Instructional exposition (textbooks, tutorial papers, etc.)
| 13-02 |
Research exposition (monographs, survey articles)
| 13-03 |
Historical (must also be assigned at least one classification number from Section 01)
| 13-04 |
Explicit machine computation and programs (not the theory of computation or programming)
| 13-06 |
Proceedings, conferences, collections, etc.
| |
13Axx |
General commutative ring theory
| 13A02 |
Graded rings [See also 16W50]
| 13A05 |
Divisibility
| 13A10 |
Radical theory
| 13A15 |
Ideals; multiplicative ideal theory
| 13A18 |
Valuations and their generalizations [See also 12J20]
[xref: 12J20, 13F30]
| 13A30 |
Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
| 13A35 |
Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$ ; tight closure [See also 13B22]
[xref: 13B22]
| 13A50 |
Actions of groups on commutative rings; invariant theory [See also 14L24]
[xref: 14L24, 14L30, 14R20]
| 13A99 |
None of the above, but in this section
| |
13Bxx |
Ring extensions and related topics
| 13B02 |
Extension theory
| 13B05 |
Galois theory
| 13B10 |
Morphisms
integral closure; integrally closed rings, related rings (Japanese, etc.)
| 13B21 |
Integral dependence
| 13B22 |
Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
[xref: 13A35]
| 13B24 |
Going up; going down; going between
| 13B25 |
Polynomials over commutative rings [See also 11C08, 13F20, 13M10]
[xref: 13F20]
| 13B30 |
Quotients and localization
| 13B35 |
Completion [See also 13J10]
[xref: 13J10]
| 13B40 |
Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
[xref: 13J15, 14B12, 14B25]
| 13B99 |
None of the above, but in this section
| |
13Cxx |
Theory of modules and ideals
| 13C05 |
Structure, classification theorems
| 13C10 |
Projective and free modules and ideals [See also 19A13]
[xref: 18G05, 19A13]
| 13C11 |
Injective and flat modules and ideals
[xref: 18G05]
| 13C12 |
Torsion modules and ideals
[xref: 13D30]
| 13C13 |
Other special types
| 13C14 |
Cohen-Macaulay modules [See also 13H10]
| 13C15 |
Dimension theory, depth, related rings (catenary, etc.)
| 13C20 |
Class groups [See also 11R29]
| 13C40 |
Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]
[xref: 14M06, 14M10, 14M12]
| 13C99 |
None of the above, but in this section
| |
13Dxx |
Homological methods {For noncommutative rings, see 16Exx ; for general categories, see 18Gxx}
[xref: 14Fxx, 18Gxx]
| 13D02 |
Syzygies and resolutions
[xref: 18G10]
| 13D03 |
(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
| 13D05 |
Homological dimension
[xref: 18G20]
| 13D07 |
Homological functors on modules (Tor, Ext, etc.)
| 13D10 |
Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]
[xref: 14B10, 14B12, 14D15, 16S80, 32G05]
| 13D15 |
Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]
[xref: 18F25, 18F30, 19Axx, 19D50]
| 13D22 |
Homological conjectures (intersection theorems)
| 13D25 |
Complexes
| 13D30 |
Torsion theory [See also 13C12, 18E40]
[xref: 16S90, 18E40]
| 13D40 |
Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
| 13D45 |
Local cohomology [See also 14B15]
[xref: 14B15]
| 13D99 |
None of the above, but in this section
| |
13Exx |
Chain conditions, finiteness conditions
| 13E05 |
Noetherian rings and modules
| 13E10 |
Artinian rings and modules, finite-dimensional algebras
| 13E15 |
Rings and modules of finite generation or presentation; number of generators
| 13E99 |
None of the above, but in this section
| |
13Fxx |
Arithmetic rings and other special rings
| 13F05 |
Dedekind, Prüfer and Krull rings and their generalizations
| 13F07 |
Euclidean rings and generalizations
| 13F10 |
Principal ideal rings
| 13F15 |
Factorial rings, unique factorization domains [See also 14M05]
| 13F20 |
Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
[xref: 11C08, 13B25, 13P10, 52B20]
| 13F25 |
Formal power series rings [See also 13J05]
[xref: 13J05]
| 13F30 |
Valuation rings [See also 13A18]
| 13F40 |
Excellent rings
| 13F45 |
Seminormal rings
[xref: 14M05]
| 13F50 |
Rings with straightening laws, Hodge algebras
| 13F55 |
Face and Stanley-Reisner rings; simplicial complexes [See also 55U10]
| 13F99 |
None of the above, but in this section
| |
13G05 |
Integral domains
| |
13Hxx |
Local rings and semilocal rings
[xref: 14H20, 52B20]
| 13H05 |
Regular local rings
| 13H10 |
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
[xref: 13C14, 14M05]
| 13H15 |
Multiplicity theory and related topics [See also 14C17]
[xref: 14C17]
| 13H99 |
None of the above, but in this section
| |
13Jxx |
Topological rings and modules [See also 16W60, 16W80]
[xref: 16W60, 16W80]
| 13J05 |
Power series rings [See also 13F25]
[xref: 13F25]
| 13J07 |
Analytical algebras and rings [See also 32B05]
| 13J10 |
Complete rings, completion [See also 13B35]
[xref: 13B35]
| 13J15 |
Henselian rings [See also 13B40]
[xref: 13B40]
| 13J20 |
Global topological rings
| 13J25 |
Ordered rings [See also 06F25]
| 13J30 |
Real algebra [See also 12D15, 14Pxx]
| 13J99 |
None of the above, but in this section
| |
13K05 |
Witt vectors and related rings
| |
13L05 |
Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
[xref: 03C60, 03H15]
| |
13Mxx |
Finite commutative rings {For number-theoretic aspects, see 11Txx}
| 13M05 |
Structure
| 13M10 |
Polynomials
[xref: 13B25]
| 13M99 |
None of the above, but in this section
| |
13Nxx |
Differential algebra [See also 12H05, 14F10]
[xref: 12H05, 14F10]
| 13N05 |
Modules of differentials
| 13N10 |
Rings of differential operators and their modules [See also 16S32, 32C38]
[xref: 16S32]
| 13N15 |
Derivations
| 13N99 |
None of the above, but in this section
| |
13Pxx |
Computational aspects of commutative algebra [See also 68W30]
[xref: 14Qxx, 68W30]
| 13P05 |
Polynomials, factorization [See also 12Y05]
| 13P10 |
Polynomial ideals, Gröbner bases [See also 13F20]
| 13P99 |
None of the above, but in this section
| |