13XX COMMUTATIVE RINGS AND ALGEBRAS
 1300 General reference works (handbooks, dictionaries, bibliographies, etc.)
 1301 Instructional exposition (textbooks, tutorial papers, etc.)
 1302 Research exposition (monographs, survey articles)
 1303 Historical (must also be assigned at least one classification number from Section 01)
 1304 Explicit machine computation and programs (not the theory of computation or programming)
 1306 Proceedings, conferences, collections, etc.
 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
 13Gxx Integral domains
 13Hxx Local rings and semilocal rings

13Jxx Topological rings and modules [See also 16W60, 16W80]
(1)
 13Lxx Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
 13Mxx Finite commutative rings (For numbertheoretic aspects, see 11Txx)
 13Nxx Differential algebra [See also 12H05, 14F10]

13Pxx Computational aspects and applications [See also 14Qxx, 68W30]
(1)