Mathematics Subject Classification 1991

12-XX Field theory and polynomials ( 0 Dok.)

• 12-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 12-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 12-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 12-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 12-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 12-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 12Dxx Real and complex fields ( 0 Dok. )
• 12D05 Polynomials: factorization ( 0 Dok.)
• 12D10 Polynomials: location of zeros (algebraic theorems), {For the analytic theory, See 26C10, 30C15} ( 0 Dok.)
• 12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), See also {11Exx} ( 0 Dok.)
• 12D99 None of the above but in this section ( 0 Dok.)
• 12Exx General field theory ( 0 Dok. )
• 12E05 Polynomials (irreducibility, etc.) ( 0 Dok.)
• 12E10 Special polynomials ( 0 Dok.)
• 12E12 Equations ( 0 Dok.)
• 12E15 Skew fields, division rings, See also {11R52, 11R54, 11S45, 16Kxx} ( 0 Dok.)
• 12E20 Finite fields (field-theoretic aspects) ( 0 Dok.)
• 12E25 Hilbertian fields; Hilbert's irreducibility theorem ( 0 Dok.)
• 12E99 None of the above but in this section ( 0 Dok.)
• 12Fxx Field extensions ( 0 Dok. )
• 12F05 Algebraic extensions ( 0 Dok.)
• 12F10 Separable extensions, Galois theory ( 0 Dok.)
• 12F12 Inverse Galois theory ( 0 Dok.)
• 12F15 Inseparable extensions ( 0 Dok.)
• 12F20 Transcendental extensions ( 0 Dok.)
• 12F99 None of the above but in this section ( 0 Dok.)
• 12Gxx Homological methods (field theory) ( 0 Dok. )
• 12G05 Galois cohomology, See also {13A20, 16H05} ( 0 Dok.)
• 12G10 Cohomological dimension ( 0 Dok.)
• 12G99 None of the above but in this section ( 0 Dok.)
• 12Hxx Differential and difference algebra ( 0 Dok. )
• 12H05 Differential algebra, See also {13Nxx} ( 0 Dok.)
• 12H10 Difference algebra, See also {39Axx} ( 0 Dok.)
• 12H20 Abstract differential equations, See also {34Gxx} ( 0 Dok.)
• 12H25 $p$-adic differential equations, See also {11S80, 14G20, 34Gxx} ( 0 Dok.)
• 12H99 None of the above but in this section ( 0 Dok.)
• 12Jxx Topological fields ( 0 Dok. )
• 12J05 Normed fields ( 0 Dok.)
• 12J10 Valued fields ( 0 Dok.)
• 12J12 Formally $p$-adic fields ( 0 Dok.)
• 12J15 Ordered fields ( 0 Dok.)
• 12J17 Topological semifields ( 0 Dok.)
• 12J20 General valuation theory ( 0 Dok.)
• 12J25 Non-Archimedean valued fields, See also {30G06, 32P05, 46S10, 47S10} ( 0 Dok.)
• 12J27 Krasner-Tate algebras See mainly{ 32P05; See also 46S10, 47S10} ( 0 Dok.)
• 12J99 None of the above but in this section ( 0 Dok.)
• 12Kxx Generalizations of fields ( 0 Dok. )
• 12K05 Near-fields, See also {16Y30} ( 0 Dok.)
• 12K10 Semifields, See also {16Y60} ( 0 Dok.)
• 12K99 None of the above but in this section ( 0 Dok.)
• 12Lxx Connections with logic ( 0 Dok. )
• 12L05 Decidability, See also {03B25} ( 0 Dok.)
• 12L10 Ultraproducts, See also {03C20} ( 0 Dok.)
• 12L12 Model theory, See also {03C60} ( 0 Dok.)
• 12L15 Nonstandard arithmetic, See also {03H15} ( 0 Dok.)
• 12L99 None of the above but in this section ( 0 Dok.)
• 12Y05 Computational aspects of field theory and polynomials ( 0 Dok.)