| 12-XX |
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Field theory and polynomials |
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12-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory |
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12-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory |
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12-02 |
Research exposition (monographs, survey articles) pertaining to field theory |
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12-03 |
History of field theory [Consider also classification numbers from Section 01-XX] |
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12-04 |
Software, source code, etc. for problems pertaining to field theory |
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12-06 |
Proceedings, conferences, collections, etc. pertaining to field theory |
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12D05 |
Polynomials in real and complex fields: factorization |
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12D10 |
Polynomials in real and complex fields: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15} |
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12D15 |
Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx] |
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12D99 |
None of the above, but in this section |
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12E05 |
Polynomials in general fields (irreducibility, etc.) |
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12E10 |
Special polynomials in general fields |
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12E12 |
Equations in general fields |
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12E15 |
Skew fields, division rings [See also 11R52, 16Kxx] |
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12E20 |
Finite fields (field-theoretic aspects) |
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12E25 |
Hilbertian fields; Hilbert's irreducibility theorem |
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12E30 |
Field arithmetic |
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12E99 |
None of the above, but in this section |
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12F05 |
Algebraic field extensions |
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12F10 |
Separable extensions, Galois theory |
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12F12 |
Inverse Galois theory |
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12F15 |
Inseparable field extensions |
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12F20 |
Transcendental field extensions |
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12F99 |
None of the above, but in this section |
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12G05 |
Galois cohomology [See also 14F22, 16H05, 16K50] |
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12G10 |
Cohomological dimension of fields |
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12G99 |
None of the above, but in this section |
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12H05 |
Differential algebra [See also 13Nxx] |
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12H10 |
Difference algebra [See also 39Axx] |
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12H20 |
Abstract differential equations [See also 34Mxx] |
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12H25 |
$p$-adic differential equations [See also 11S80, 14G20] |
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12H99 |
None of the above, but in this section |
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12J05 |
Normed fields |
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12J10 |
Valued fields |
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12J12 |
Formally $p$-adic fields |
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12J15 |
Ordered fields |
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12J17 |
Topological semifields |
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12J20 |
General valuation theory for fields [See also 13A18] |
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12J25 |
Non-Archimedean valued fields [See also 30G06, 46S10] |
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12J27 |
Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10] |
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12J99 |
None of the above, but in this section |
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12K05 |
Near-fields [See also 16Y30] |
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12K10 |
Semifields [See also 16Y60] |
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12K99 |
None of the above, but in this section |
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12L05 |
Decidability and field theory [See also 03B25] |
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12L10 |
Ultraproducts and field theory [See also 03C20] |
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12L12 |
Model theory of fields [See also 03C60] |
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12L15 |
Nonstandard arithmetic and field theory [See also 03H15] |
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12L99 |
None of the above, but in this section |
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12Y05 |
Computational aspects of field theory and polynomials |
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12Y99 |
None of the above, but in this section |
