La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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13-XX 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 (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.
• 13-99 Commutative rings and algebras (not classified at a more specific level)
• 13Axx General commutative ring theory
• 13Bxx Ring extensions and related topics
• 13Cxx Theory of modules and ideals
• 13Dxx 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 (Co)homological dimensions [See also 18G20]
  • 13D07 Homological functors on modules (Tor, Ext, etc.) [See also 18G15] [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 13D02, 13D05
  • 13D10 Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 16S80, 32Gxx]
  • 13D15 Grothendieck groups, K-theory [See also 14C35, 18F25, 18F30, 19Axx, 19D50]
  • 13D22 Homological conjectures (intersection theorems) [Nouveau code MSC 2000]
    • Codes MSC1991 affiliés : 13D03, 13H15
  • 13D25 Complexes
  • 13D30 Torsion theory [See also 13C12, 16S90, 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
• 13Exx Chain conditions, finiteness conditions
• 13Fxx Arithmetic rings and other special rings
• 13G05 Integral domains
• 13Hxx Local rings and semilocal rings
• 13Jxx Topological rings and modules [See also 16W80]
• 13K05 Witt vectors and related rings
• 13L05 Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
• 13Mxx Finite commutative rings [See also 13A35; for number-theoretic aspects, see 11Txx]
• 13Nxx Differential algebra [See also 12H05, 14F10]
• 13Pxx Computational aspects of commutative algebra [See also 68W30]

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