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Biblioteca Dr. Antonio Monteiro · Catálogo |
| 12 | 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 | ||
| 12-04 | Explicit machine computation and programs (not the theory of computation or programming) | ||
| 12-06 | Proceedings, conferences, collections, etc. | ||
| 12-99 | Field theory and polynomials (not classified at a more specific level) | ||
| 12D | 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 | ||
| 12E | 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 | ||
| 12F | 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 | ||
| 12G | Homological methods (field theory) | ||
| 12G05 | Galois cohomology [See also 14F22, 16H05, 16K50] | ||
| 12G10 | Cohomological dimension | ||
| 12G99 | None of the above, but in this section | ||
| 12H | 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] | ||
| 12H99 | None of the above, but in this section | ||
| 12J | 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 | ||
| 12K | Generalizations of fields | ||
| 12K05 | Near-fields [See also 16Y30] | ||
| 12K10 | Semifields [See also 16Y60] | ||
| 12K99 | None of the above, but in this section | ||
| 12L | 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 | ||
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