Classification Search Result - zbMATH Open

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Mathematics Subject Classification – MSC2020

Commutative algebra

40878

Theory of modules and ideals in commutative rings

8208

Structure, classification theorems for modules and ideals in commutative rings

1778

Projective and free modules and ideals in commutative rings [See also 19A13]

1478

Injective and flat modules and ideals in commutative rings

705

Torsion modules and ideals in commutative rings

279

Other special types of modules and ideals in commutative rings

1064

Cohen-Macaulay modules [See also 13H10]

1025

Dimension theory, depth, related commutative rings (catenary, etc.)

1451

Class groups [See also 11R29]

237

Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]

816

Module categories and commutative rings

131

Theory of modules and ideals in commutative rings described by combinatorial properties [See also 05C25, 05E40]

14

None of the above, but in this section

606

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

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