Mathematics Subject Classification 1991

13-XX Commutative rings and algebras ( 0 Dok.)

• 13-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 13-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 13-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 13-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 13-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 13-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 13Axx General commutative ring theory ( 0 Dok. )
• 13A02 Graded rings, See also {16W50} ( 0 Dok.)
• 13A05 Divisibility ( 0 Dok.)
• 13A10 Radical theory ( 0 Dok.)
• 13A15 Ideals; multiplicative ideal theory ( 0 Dok.)
• 13A18 Valuations and their generalizations ( 0 Dok.)
• 13A20 Brauer groups, See also {12Gxx, 16H05} ( 0 Dok.)
• 13A30 Associated graded rings of ideals (Rees ring, form ring) and related topics ( 0 Dok.)
• 13A35 Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$, See also {13Mxx} ( 0 Dok.)
• 13A50 Invariant theory, See also {14D25} ( 0 Dok.)
• 13A99 None of the above but in this section ( 0 Dok.)
• 13Bxx Ring extensions and related topics ( 0 Dok. )
• 13B02 Extension theory ( 0 Dok.)
• 13B05 Galois theory (commutative rings) ( 0 Dok.)
• 13B10 Morphisms and derivations ( 0 Dok.)
• 13B15 Ramification theory ( 0 Dok.)
• 13B21 Integral dependence ( 0 Dok.)
• 13B22 Integral closure; integrally closed rings, related rings (Japanese, etc.) ( 0 Dok.)
• 13B24 Going up; going down; going between ( 0 Dok.)
• 13B25 Polynomials over commutative rings ( 0 Dok.)
• 13B30 Quotients and localization ( 0 Dok.)
• 13B35 Completion, See also {13J10} ( 0 Dok.)
• 13B40 Etale extensions and Henselization; Artin approximation, See also {13J15, 14B12} ( 0 Dok.)
• 13B99 None of the above but in this section ( 0 Dok.)
• 13Cxx Theory of modules and ideals ( 0 Dok. )
• 13C05 Structure, classification theorems ( 0 Dok.)
• 13C10 Projective and free modules and ideals, See also {18G05, 19A13} ( 0 Dok.)
• 13C11 Injective and flat modules and ideals, See also {18G05} ( 0 Dok.)
• 13C12 Torsion modules and ideals ( 0 Dok.)
• 13C13 Other special types ( 0 Dok.)
• 13C14 Cohen-Macaulay modules, See also {13H10} ( 0 Dok.)
• 13C15 Dimension theory, depth, related rings (catenary, etc.) ( 0 Dok.)
• 13C20 Class groups ( 0 Dok.)
• 13C40 Linkage, complete intersections and determinantal ideals, See also {14M12} ( 0 Dok.)
• 13C99 None of the above but in this section ( 0 Dok.)
• 13Dxx (Co)homological methods ( 0 Dok. )
• 13D02 Syzygies ( 0 Dok.)
• 13D03 (Co)homology of commutative rings and algebras ( 0 Dok.)
• 13D05 (Co)homological dimension, See also {18G20} ( 0 Dok.)
• 13D10 Deformations and infinitesimal methods, See also {14B12, 14D15, 16S80, 32Gxx} ( 0 Dok.)
• 13D15 Grothendieck groups, $K$-theory, See also {14C35, 18F30, 19-XX} ( 0 Dok.)
• 13D25 Complexes ( 0 Dok.)
• 13D30 Torsion theory, See also {13C12, 18E40} ( 0 Dok.)
• 13D40 Hilbert-Samuel functions and Poincare series ( 0 Dok.)
• 13D45 Local cohomology, See also {14B15} ( 0 Dok.)
• 13D99 None of the above but in this section ( 0 Dok.)
• 13Exx Chain conditions, finiteness conditions ( 0 Dok. )
• 13E05 Noetherian rings and modules ( 0 Dok.)
• 13E10 Artinian rings and modules, finite-dimensional algebras ( 0 Dok.)
• 13E15 Rings and modules of finite generation or presentation ( 0 Dok.)
• 13E99 None of the above but in this section ( 0 Dok.)
• 13Fxx Arithmetic rings and other special rings, See also {12-XX} ( 0 Dok. )
• 13F05 Dedekind and Prufer rings and their generalizations ( 0 Dok.)
• 13F07 Euclidean rings and generalizations ( 0 Dok.)
• 13F10 Principal ideal rings ( 0 Dok.)
• 13F15 Factorial rings, unique factorization domains, See Also { 14M05} ( 0 Dok.)
• 13F20 Polynomial rings and ideals, See also {11C08} ( 0 Dok.)
• 13F25 Formal power series rings, See also {13J05} ( 0 Dok.)
• 13F30 Valuation rings ( 0 Dok.)
• 13F40 Excellent rings ( 0 Dok.)
• 13F45 Seminormal rings ( 0 Dok.)
• 13F50 Rings with straightening laws, Hodge algebras ( 0 Dok.)
• 13F99 None of the above but in this section ( 0 Dok.)
• 13G05 Integral domains ( 0 Dok.)
• 13Hxx Local rings and semilocal rings ( 0 Dok. )
• 13H05 Regular local rings ( 0 Dok.)
• 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), See also {14M05} ( 0 Dok.)
• 13H15 Multiplicity theory and related topies ( 0 Dok.)
• 13H99 None of the above but in this section ( 0 Dok.)
• 13Jxx Topological rings and modules, See also {16W60, 16W80} ( 0 Dok. )
• 13J05 Power series rings, See also {13F25} ( 0 Dok.)
• 13J07 Analytical algebras and rings, See also {32B05} ( 0 Dok.)
• 13J10 Complete rings, completion, See also {13B35} ( 0 Dok.)
• 13J15 Henselian rings, See also {13B40} ( 0 Dok.)
• 13J20 Global topological rings ( 0 Dok.)
• 13J25 Ordered rings, See also {06F25} ( 0 Dok.)
• 13J99 None of the above but in this section ( 0 Dok.)
• 13K05 Witt vectors and related rings ( 0 Dok.)
• 13L05 Applications of logic to commutative algebra, See Also { 03Cxx, 03Hxx} ( 0 Dok.)
• 13Mxx Finite commutative rings, {For number-theoretic aspects, See 11Txx} ( 0 Dok. )
• 13M05 Structure ( 0 Dok.)
• 13M10 Polynomials (commutative rings) ( 0 Dok.)
• 13M99 None of the above but in this section ( 0 Dok.)
• 13Nxx Differential algebra, See also {12H05, 14F10} ( 0 Dok. )
• 13N05 Modules of differentials, See also {16S32} ( 0 Dok.)
• 13N10 Rings of differential operators, See also {16S32, 32C38} ( 0 Dok.)
• 13N99 None of the above but in this section ( 0 Dok.)
• 13Pxx Computational aspects of commutative algebra, See Also { 68Q40} ( 0 Dok. )
• 13P05 Polynomials, factorization, See also {12Y05} ( 0 Dok.)
• 13P10 Polynomial ideals, Grobner bases ( 0 Dok.)
• 13P99 None of the above but in this section ( 0 Dok.)