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
|