12-XX Field theory and polynomials
12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
12-01 Instructional exposition (textbooks, tutorial papers, etc.)
12-02 Research exposition (monographs, survey articles)
12-03 Historical {!must also be assigned at least one classification number from section 01}
12-04 Explicit machine computation and programs (not the theory of computation or programming)
12-06 Proceedings, conferences, collections, etc.
12Dxx Real and complex fields
12D05 Polynomials: factorization
12D10 Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15}
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
12D99 None of the above, but in this section
12Exx General field theory
12E05 Polynomials (irreducibility, etc.)
12E10 Special polynomials
12E12 Equations
12E15 Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]
12E20 Finite fields (field-theoretic aspects)
12E25 Hilbertian fields; Hilbert's irreducibility theorem
12E30 Field arithmetic
12E99 None of the above, but in this section
12Fxx Field extensions
12F05 Algebraic extensions
12F10 Separable extensions, Galois theory
12F12 Inverse Galois theory
12F15 Inseparable extensions
12F20 Transcendental extensions
12F99 None of the above, but in this section
12Gxx Homological methods (field theory)
12G05 Galois cohomology [See also 14F22, 16H05, 16K50]
12G10 Cohomological dimension
12G99 None of the above, but in this section
12Hxx Differential and difference algebra
12H05 Differential algebra [See also 13Nxx]
12H10 Difference algebra [See also 39Axx]
12H20 Abstract differential equations [See also 34Mxx]
12H25 p-adic differential equations [See also 11S80, 14G20, 34Gxx]
12H99 None of the above, but in this section
12Jxx Topological fields
12J05 Normed fields
12J10 Valued fields
12J12 Formally p-adic fields
12J15 Ordered fields
12J17 Topological semifields
12J20 General valuation theory [See also 13A18]
12J25 Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
12J27 Krasner - Tate algebras [See mainly 32P05; see also 46S10, 47S10]
12J99 None of the above, but in this section
12Kxx Generalizations of fields
12K05 Near-fields [See also 16Y30]
12K10 Semifields [See also 16Y60]
12K99 None of the above, but in this section
12Lxx Connections with logic
12L05 Decidability [See also 03B25]
12L10 Ultraproducts [See also 03C20]
12L12 Model theory [See also 03C60]
12L15 Nonstandard arithmetic [See also 03H15]
12L99 None of the above, but in this section
12Y05 Computational aspects of field theory and polynomials