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Navegando por la clasificación temática MSC 2000: 13 · Commutative rings and algebras
 
13 Commutative rings and algebras
  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
  13-04 Explicit machine computation and programs (not the theory of computation or programming)
  13-06 Proceedings, conferences, collections, etc.
  13-99 Commutative rings and algebras (not classified at a more specific level)
 
  13A 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]
    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]
    13A50 Actions of groups on commutative rings; invariant theory [See also 14L24]
    13A99 None of the above, but in this section
 
  13B Ring extensions and related topics
    13B02 Extension theory
    13B05 Galois theory
    13B10 Morphisms
    13B21 Integral dependence
    13B22 Integral closure of rings and ideals [See also 13A35]
    13B24 Going up; going down; going between
    13B25 Polynomials over commutative rings [See also 11C08, 13F20, 13M10]
    13B30 Quotients and localization
    13B35 Completion [See also 13J10]
    13B40 Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
    13B99 None of the above, but in this section
 
  13C Theory of modules and ideals
    13C05 Structure, classification theorems
    13C10 Projective and free modules and ideals [See also 19A13]
    13C11 Injective and flat modules and ideals
    13C12 Torsion modules and ideals
    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]
    13C99 None of the above, but in this section
 
  13D Homological methods {For noncommutative rings, see 16Exx; for general categories, see 18Gxx}
    13D02 Syzygies and resolutions
    13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
    13D05 Homological dimension
    13D07 Homological functors on modules (Tor, Ext, etc.)
    13D10 Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]
    13D15 Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]
    13D22 Homological conjectures (intersection theorems)
    13D25 Complexes
    13D30 Torsion theory [See also 13C12, 18E40]
    13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
    13D45 Local cohomology [See also 14B15]
    13D99 None of the above, but in this section
 
  13E 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
 
  13F 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]
    13F25 Formal power series rings [See also 13J05]
    13F30 Valuation rings [See also 13A18]
    13F40 Excellent rings
    13F45 Seminormal rings
    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
 
 
  13H Local rings and semilocal rings
    13H05 Regular local rings
    13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
    13H15 Multiplicity theory and related topics [See also 14C17]
    13H99 None of the above, but in this section
 
  13J Topological rings and modules [See also 16W60, 16W80]
    13J05 Power series rings [See also 13F25]
    13J07 Analytical algebras and rings [See also 32B05]
    13J10 Complete rings, completion [See also 13B35]
    13J15 Henselian rings [See also 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]
 
 
  13M Finite commutative rings {For number-theoretic aspects, see 11Txx}
    13M05 Structure
    13M10 Polynomials
    13M99 None of the above, but in this section
 
  13N Differential algebra [See also 12H05, 14F10]
    13N05 Modules of differentials
    13N10 Rings of differential operators and their modules [See also 16S32, 32C38]
    13N15 Derivations
    13N99 None of the above, but in this section
 
  13P Computational aspects of commutative algebra [See also 68W30]
    13P05 Polynomials, factorization [See also 12Y05]
    13P10 Polynomial ideals, Gröbner bases [See also 13F20]
    13P99 None of the above, but in this section
 

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