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Mathematics Subject Classification – MSC2020

Field theory and polynomials 18785

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to field theory 9

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory 751

Research exposition (monographs, survey articles) pertaining to field theory 309

History of field theory [Consider also classification numbers pertaining to Section 01-XX] 359

Software, source code, etc. for problems pertaining to field theory 390

Proceedings, conferences, collections, etc. pertaining to field theory 231

Computational methods for problems pertaining to field theory 17

Research data for problems pertaining to field theory 0

Real and complex fields 3076

Polynomials in real and complex fields: factorization 647

Polynomials in real and complex fields: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15} 1325

Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx] 799

None of the above, but in this section 376

General field theory 3650

Polynomials in general fields (irreducibility, etc.) 1105

Special polynomials in general fields 528

Equations in general fields 572

Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx] 577

Finite fields (field-theoretic aspects) 585

Hilbertian fields; Hilbert’s irreducibility theorem 173

Field arithmetic 183

None of the above, but in this section 175

Field extensions 3658

Algebraic field extensions 559

Separable extensions, Galois theory 1946

Inverse Galois theory 655

Inseparable field extensions 206

Transcendental field extensions 521

None of the above, but in this section 200

Homological methods (field theory) 828

Galois cohomology [See also 14F22, 16Hxx, 16K50] 745

Cohomological dimension of fields 68

None of the above, but in this section 34

Differential and difference algebra 2384

Differential algebra [See also 13Nxx] 1593

Difference algebra [See also 39Axx] 272

Abstract differential equations [See also 34Mxx] 361

\(p\)-adic differential equations [See also 11S80, 14G20] 307

None of the above, but in this section 46

Topological fields 3019

Normed fields 63

Valued fields 1132

Formally \(p\)-adic fields 102

Ordered fields 746

Topological semifields 20

General valuation theory for fields [See also 13A18] 417

Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] 764

Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10] 45

None of the above, but in this section 170

Generalizations of fields 866

Near-fields [See also 16Y30] 381

Semifields [See also 16Y60] 335

None of the above, but in this section 160

Connections between field theory and logic 1149

Decidability and field theory [See also 03B25] 233

Ultraproducts and field theory [See also 03C20] 88

Model theory of fields [See also 03C60] 724

Nonstandard arithmetic and field theory [See also 03H15] 77

None of the above, but in this section 97

Commutative algebra 37830

Computational aspects and applications of commutative rings [See also 14Qxx, 68W30] {For software etc., see 13-04} 4623

Polynomials, factorization in commutative rings [See also 12-08] 401

Algebraic geometry 84974

Computational aspects in algebraic geometry {For software etc., see 14-04} [See also 12-08, 13Pxx, 68W30] 2503

Computational aspects of algebraic curves [See also 14Hxx] 969

Computational aspects of algebraic surfaces [See also 14Jxx] 423

Computational aspects of higher-dimensional varieties [See also 14Jxx, 14Mxx] 358

Effectivity, complexity and computational aspects of algebraic geometry 354

Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx] 1

Computational real algebraic geometry [See also 14Pxx] 11

Geometric aspects of numerical algebraic geometry [See also 65H14] 31

None of the above, but in this section 415

Category theory; homological algebra {For commutative rings, see 13Dxx; for associative rings, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} 28352

Categories in geometry and topology 3822

Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 1799

Computer science {For papers containing software, source code, etc. in a specific mathematical area, see the classification number -04 in that area} 358706

Algorithms in computer science {For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx} 47808

Symbolic computation and algebraic computation [See also 11Yxx, 12-08, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 11090

Overview

00

General and overarching topics; collections

01

History and biography

03

Mathematical logic and foundations

05

Combinatorics

06

Order, lattices, ordered algebraic structures

08

General algebraic systems

11

Number theory

12

Field theory and polynomials

13

Commutative algebra

14

Algebraic geometry

15

Linear and multilinear algebra; matrix theory

16

Associative rings and algebras

17

Nonassociative rings and algebras

18

Category theory; homological algebra

19

\(K\)-theory

20

Group theory and generalizations

22

Topological groups, Lie groups

26

Real functions

28

Measure and integration

30

Functions of a complex variable

31

Potential theory

32

Several complex variables and analytic spaces

33

Special functions

34

Ordinary differential equations

35

Partial differential equations

37

Dynamical systems and ergodic theory

39

Difference and functional equations

40

Sequences, series, summability

41

Approximations and expansions

42

Harmonic analysis on Euclidean spaces

43

Abstract harmonic analysis

44

Integral transforms, operational calculus

45

Integral equations

46

Functional analysis

47

Operator theory

49

Calculus of variations and optimal control; optimization

51

Geometry

52

Convex and discrete geometry

53

Differential geometry

54

General topology

55

Algebraic topology

57

Manifolds and cell complexes

58

Global analysis, analysis on manifolds

60

Probability theory and stochastic processes

62

Statistics

65

Numerical analysis

68

Computer science

70

Mechanics of particles and systems

74

Mechanics of deformable solids

76

Fluid mechanics

78

Optics, electromagnetic theory

80

Classical thermodynamics, heat transfer

81

Quantum theory

82

Statistical mechanics, structure of matter

83

Relativity and gravitational theory

85

Astronomy and astrophysics

86

Geophysics

90

Operations research, mathematical programming

91

Game theory, economics, finance, and other social and behavioral sciences

92

Biology and other natural sciences

93

Systems theory; control

94

Information and communication theory, circuits

97

Mathematics education

W3C

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