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]
• 13Exx Chain conditions, finiteness conditions
• 13Fxx Arithmetic rings and other special rings
• 13G05 Integral domains
• 13Hxx Local rings and semilocal rings
  • 13H05 Regular local rings
  • 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 13C14, 14M05]
  • 13H15 Multiplicity theory and related topics [See also 14C17]
  • 13H99 None of the above, but in this section
• 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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