| 12-XX | | Prev: 11 | Up: Top | Next: 13 | |
| Field theory and polynomials [xref: 18F25] |
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
[xref: 14P05, 26C05]
| 12D05 |
Polynomials: factorization
| 12D10 |
Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15}
[xref: 26C10]
| 12D15 |
Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
[xref: 13J30]
| 12D99 |
None of the above, but in this section
| |
12Exx |
General field theory
[xref: 26C05]
| 12E05 |
Polynomials (irreducibility, etc.)
| 12E10 |
Special polynomials
| 12E12 |
Equations
| 12E15 |
Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]
[xref: 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
[xref: 20B25, 20B27]
| 12F12 |
Inverse Galois theory
| 12F15 |
Inseparable extensions
| 12F20 |
Transcendental extensions
| 12F99 |
None of the above, but in this section
| |
12Gxx |
Homological methods (field theory)
[xref: 11R34, 11S25]
| 12G05 |
Galois cohomology [See also 14F22, 16H05, 16K50]
[xref: 14F22, 16K50]
| 12G10 |
Cohomological dimension
| 12G99 |
None of the above, but in this section
| |
12Hxx |
Differential and difference algebra
| 12H05 |
Differential algebra [See also 13Nxx]
[xref: 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
| |
12Jxx |
Topological fields
[xref: 54H13]
| 12J05 |
Normed fields
| 12J10 |
Valued fields
| 12J12 |
Formally $p$-adic fields
| 12J15 |
Ordered fields
[xref: 11R80]
| 12J17 |
Topological semifields
| 12J20 |
General valuation theory [See also 13A18]
[xref: 13A18]
| 12J25 |
Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
[xref: 26E30, 30G06, 46S10]
| 12J27 |
Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]
| 12J99 |
None of the above, but in this section
| |
12Kxx |
Generalizations of fields
[xref: 51A25]
| 12K05 |
Near-fields [See also 16Y30]
[xref: 16Y30, 51J20]
| 12K10 |
Semifields [See also 16Y60]
[xref: 16Y60]
| 12K99 |
None of the above, but in this section
| |
12Lxx |
Connections with logic
[xref: 03C60]
| 12L05 |
Decidability [See also 03B25]
[xref: 03B25]
| 12L10 |
Ultraproducts [See also 03C20]
| 12L12 |
Model theory [See also 03C60]
| 12L15 |
Nonstandard arithmetic [See also 03H15]
[xref: 03H15]
| 12L99 |
None of the above, but in this section
| |
12Y05 |
Computational aspects of field theory and polynomials
[xref: 13P05, 14Qxx, 68W30]
| |