La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

Question : CC = Ore
00-XX General

• 00-99 General mathematics (not classified at a more specific level)
• 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)

01-XX History and biography

• 01-99 History and biography (not classified at a more specific level)

03-XX Mathematical logic and foundations

• 03-99 Mathematical logic and foundations (not classified at a more specific level)
• 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) [For proof-theoretic aspects see 03F52] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 03B46, 03F50
• 03C25 Model-theoretic forcing
• 03C55 Set-theoretic model theory
• 03C57 Effective and recursion-theoretic model theory [See also 03D45]
• 03C60 Model-theoretic algebra [See also 08C10, 11U09, 12L12, 13L05, 16B70, 20A15]
• 03E45 Inner models, including constructibility, ordinal definability, and core models
• 03E47 Other notions of set-theoretic definability
• 03F05 Cut-elimination and normal-form theorems

05-XX Combinatorics [For finite fields, see 11Txx]

• 05-99 Combinatorics (not classified at a more specific level)
• 05B10 Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]

06-XX Order, lattices, ordered algebraic structures [See also 18B35]

• 06-99 Order, lattices, ordered algebraic structures (not classified at a more specific level)
• 06E20 Ring-theoretic properties [See also 16E50, 16G30]

08-XX General algebraic systems

• 08-99 General mathematical systems (not classified at a more specific level)

11-XX Number theory

• 11-99 Number theory (not classified at a more specific level)
• 11E20 General ternary and quaternary quadratic forms; forms of more than two variables
• 11F70 Representation-theoretic methods; automorphic representations over local and global fields
• 11H60 Mean value and transfer theorems
• 11M45 Tauberian theorems [See also 40E05]
• 11P32 Goldbach-type theorems; other additive questions involving primes
• 11R45 Density theorems
• 11Txx Finite fields and commutative rings (number-theoretic aspects) [See also 13Mxx]

12-XX Field theory and polynomials

• 12-99 Algebraic number theory, field theory and polynomials (not classified at a more specific level)
• 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]
• 12E20 Finite fields (field-theoretic aspects)
• 12E25 Hilbertian fields; Hilbert's irreducibility theorem

13-XX Commutative rings and algebras

• 13-99 Commutative rings and algebras (not classified at a more specific level)
• 13C05 Structure, classification theorems
• 13D22 Homological conjectures (intersection theorems) [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 13D03, 13H15
• 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 13C14, 14M05]
• 13Mxx Finite commutative rings [See also 13A35; for number-theoretic aspects, see 11Txx]

14-XX Algebraic geometry

• 14-99 Algebraic geometry (not classified at a more specific level)
• 14C34 Torelli problem
• 14C40 Riemann-Roch theorems [See also 19E20, 19L10]
• 14F17 Vanishing theorems [See also 32L20]

15-XX Linear and multilinear algebra; matrix theory

• 15-99 Linear and multilinear algebra; matrix theory (finite and infinite) (not classified at a more specific level)
• 15A54 Matrices over function rings in one or more variables

16-XX Associative rings and algebras [For the commutative case, see 13-XX]

• 16-99 Associative rings and algebras (not classified at a more specific level)
• 16B50 Category-theoretic methods and results (except as in 16D90) [See also 18-XX]
• 16D90 Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality
• 16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 16E99
• 16U20 Ore rings, multiplicative sets, Ore localization
• 16W35 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 16W30

17-XX Nonassociative rings and algebras

• 17-99 Nonassociative rings and algebras (not classified at a more specific level)

18-XX Category theory; homological algebra [For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology]

• 18-99 Category theory, homological algebra (not classified at a more specific level)
• 18B15 Embedding theorems, universal categories [See also 18E20]
• 18E20 Embedding theorems [See also 18B15]

19-XX $K$-theory [See also 16E20, 18F25]

• 19-99 General (not classified at a more specific level)
• 19L10 Riemann-Roch theorems, Chern characters

20-XX Group theory and generalizations

• 20-99 Group theory and generalizations (not classified at a more specific level)
• 20B10 Characterization theorems
• 20E07 Subgroup theorems; subgroup growth
• 20E34 General structure theorems
• 20E36 General theorems concerning automorphisms of groups

22-XX Topological groups, Lie groups [For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX]

• 22-99 Topological groups, Lie groups (not classified at a more specific level)
• 22D35 Duality theorems
• 22E43 Structure and representation of the Lorentz group
• 22E67 Loop groups and related constructions, group-theoretic treatment [See also 58D05]

26-XX Real functions [See also 54C30]

• 26-99 Real functions (not classified at a more specific level)
• 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
• 26B10 Implicit function theorems, Jacobians, transformations with several variables

28-XX Measure and integration [For analysis on manifolds, see 58-XX]

• 28-99 Measure and integration (not classified at a more specific level)
• 28A05 Classes of sets (Borel fields, -rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
• 28Dxx Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]

30-XX Functions of a complex variable [For analysis on manifolds, see 58-XX]

• 30-99 Functions of a complex variable (not classified at a more specific level)
• 30C25 Covering theorems in conformal mapping theory

31-XX Potential theory [For probabilistic potential theory, see 60J45]

• 31-99 Potential theory (not classified at a more specific level)
• 31A20 Boundary behavior (theorems of Fatou type, etc.)

32-XX Several complex variables and analytic spaces [For infinite-dimensional holomorphy, see 46G20, 58B12]

• 32-99 Several complex variables and analytic spaces (not classified at a more specific level)
• 32B05 Analytic algebras and generalizations, preparation theorems
• 32C37 Duality theorems
• 32F32 Analytical consequences of geometric convexity (vanishing theorems, etc.) [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 32F99, 32L20, 32L15
• 32H25 Picard-type theorems and generalizations [For function-theoretic properties, see 32A22]
• 32H30 Value distribution theory in higher dimensions [For function-theoretic properties, see 32A22]
• 32H35 Proper mappings, finiteness theorems
• 32J10 Algebraic dependence theorems
• 32L20 Vanishing theorems
• 32Q40 Embedding theorems [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 32C10
• 32Q57 Classification theorems [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 32C10, 32J15, 32J17, 32J18
• 32S50 Topological aspects: Lefschetz theorems, topological classification, invariants

33-XX Special functions (33-XX deals with the properties of functions as functions) [For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx]

• 33-99 Special functions (not classified at a more specific level)

34-XX Ordinary differential equations

• 34-99 Ordinary differential equations (not classified at a more specific level)
• 34A45 Theoretical approximation of solutions [For numerical analysis, see 65Lxx]
• 34K07 Theoretical approximation of solutions [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 34A45, 34K05, 34K99
• 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 34A20

35-XX Partial differential equations

• 35-99 Partial differential equations (not classified at a more specific level)
• 35A05 General existence and uniqueness theorems
• 35A07 Local existence and uniqueness theorems [See also 35Hxx, 35Sxx]
• 35A10 Cauchy-Kovalevskaya theorems
• 35A35 Theoretical approximation to solutions [For numerical analysis, see 65Mxx, 65Nxx]
• 35B05 General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)
• 35C10 Series solutions, expansion theorems

37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]

• 37-99 Dynamic systems and ergodic theory (not classified at a more specific level)
• 37A30 Ergodic theorems, spectral theory, Markov operators [For operator ergodic theory, see mainly 47A35] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 28D05, 28D10, 28D15, 47A35, 58F11
• 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 34C25, 34C37, 58F05, 58F14, 58F22

39-XX Difference and functional equations

• 39-99 Difference and functional equations (not classified at a more specific level)
• 39B52 Equations for functions with more general domains and/or ranges

40-XX Sequences, series, summability

• 40-99 Sequences, series, summability (not classified at a more specific level)
• 40C15 Function-theoretic methods (including power series methods and semicontinuous methods)
• 40Dxx Direct theorems on summability
• 40D05 General theorems
• 40D25 Inclusion and equivalence theorems
• 40Exx Inversion theorems
• 40E05 Tauberian theorems, general
• 40E15 Lacunary inversion theorems
• 40G10 Abel, Borel and power series methods

41-XX Approximations and expansions [For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx]

• 41-99 Approximations and expansions (not classified at a more specific level)
• 41A27 Inverse theorems

42-XX Fourier analysis

• 42-99 Fourier analysis (not classified at a more specific level)

43-XX Abstract harmonic analysis [For other analysis on topological and Lie groups, see 22Exx]

• 43-99 Abstract harmonic analysis (not classified at a more specific level)

44-XX Integral transforms, operational calculus [For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10]

• 44-99 Integral transforms (not classified at a more specific level)

45-XX Integral equations

• 45-99 Integral equations (not classified at a more specific level)
• 45L05 Theoretical approximation of solutions [For numerical analysis see 65Rxx]

46-XX Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]

• 46-99 Functional analysis (not classified at a more specific level)
• 46A19 Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than R, etc.)
• 46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
• 46A30 Open mapping and closed graph theorems; completeness (including B-, B<sub>r</sub>-completeness)
• 46E30 Spaces of measurable functions (L<sup>p</sup>-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

47-XX Operator theory

• 47-99 Operator theory (not classified at a more specific level)
• 47A30 Norms (inequalities, more than one norm, etc.)
• 47H10 Fixed-point theorems [Sse also 54H25, 55M20, 58C30]
• 47J07 Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 46G05, 47H15, 58C15

49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]

• 49-99 Calculus of variations and optimal control; optimization (not classified at a more specific level)
• 49J10 Free problems in two or more independent variables
• 49K10 Free problems in two or more independent variables
• 49Q20 Variational problems in a geometric measure-theoretic setting

51-XX Geometry [For algebraic geometry, see 14-XX]

• 51-99 Geometry (not classified at a more specific level)
• 51A20 Configuration theorems
• 51L15 n-vertex theorems via direct methods

52-XX Convex and discrete geometry

• 52-99 Convex sets and related geometric topics (not classified at a more specific level)
• 52A35 Helly-type theorems and geometric transversal theory

53-XX Differential geometry [For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx]

• 53-99 Differential geometry (not classified at a more specific level)
• 53B30 Lorentz metrics, indefinite metrics [See also 53C50]
• 53C50 Lorentz manifolds, manifolds with indefinite metrics [See also 53B30]

54-XX General topology [For the topology of manifolds of all dimensions, see 57Nxx]

• 54-99 General topology (not classified at a more specific level)
• 54E30 Moore spaces
• 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
• 54H25 Fixed-point and coincidence theorems [See also 47H10, 55M20]

55-XX Algebraic topology

• 55-99 Algebraic topology (not classified at a more specific level)
• 55N40 Axioms for homology theory and uniqueness theorems
• 55T20 Eilenberg-Moore spectral sequences [See also 57T35]
• 55U20 Universal coefficient theorems, Bockstein operator

57-XX Manifolds and cell complexes [For complex manifolds, see 32Qxx]

• 57-99 Manifolds and cell complexes (not classified at a more specific level)
• 57M35 Dehn's lemma, sphere theorem, loop theorem, asphericity
• 57T35 Applications of Eilenberg-Moore spectral sequences [See also 55R20, 55T20]

58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]

• 58-99 Global analysis, analysis on manifolds (not classified at a more specific level)
• 58A03 Topos-theoretic approach to differentiable manifolds
• 58C15 Implicit function theorems; global Newton methods
• 58C30 Fixed point theorems on manifolds [See also 47H10]
• 58J20 Index theory and related fixed point theorems [See also 19K56, 46L80] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 58G10

60-XX Probability theory and stochastic processes [For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX]

• 60-08 Computational methods (not classified at a more specific level) [See also 65C50] [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 60-04
• 60-99 Probability theory and stochastic processes (not classified at a more specific level)
• 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
• 60Fxx Limit theorems [See also 28Dxx, 60B12]
• 60F05 Central limit and other weak theorems
• 60F15 Strong theorems
• 60F17 Functional limit theorems; invariance principles
• 60F25 L^p-limit theorems

62-XX Statistics

• 62-99 Statistics (not classified at a more specific level)
• 62B10 Information-theoretic topics [See also 94A17]
• 62Nxx Survival analysis and censored data
• 62N01 Censored data models [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 62G99, 62G05, 62G07, 62G10

65-XX Numerical analysis

• 65-99 Numerical analysis (not classified at a more specific level)
• 65Cxx Probabilistic methods, simulation and stochastic differential equations [For theoretical aspects, see 68U20 and 60H35]

68-XX Computer science [For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area]

• 68-99 Computer science (not classified at a more specific level)
• 68T15 Theorem proving (deduction, resolution, etc.) [See also 03B35]

70-XX Mechanics of particles and systems [For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX]

• 70-99 Mechanics of particles and systems (not classified at a more specific level)
• 70S20 More general nonquantum field theories [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 70G50, 81T99

74-XX Mechanics of deformable solids

• 74-99 Mechanics of deformable solids (not classified at a more specific level)

76-XX Fluid mechanics [For general continuum mechanics, see 74Axx, or other parts of 74-XX]

• 76-99 Fluid mechanics (not classified at a more specific level)
• 76F30 Renormalization and other field-theoretical methods [See also 81T99] [Nouveau code MSC 2000]
  • Codes MSC1991 affiliés : 76F99, 81T99
• 76T30 Three or more component flows [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 76T05

78-XX Optics, electromagnetic theory [For quantum optics, see 81V80]

• 78-99 Optics, electromagnetic theory (not classified at a more specific level)

80-XX Classical thermodynamics, heat transfer [For thermodynamics of solids, see 74A15]

• 80-99 Classical thermodynamics, heat transfer (not classified at a more specific level)

81-XX Quantum theory

• 81-99 Quantum mechanics (not classified at a more specific level)

82-XX Statistical mechanics, structure of matter

• 82-99 Statistical physics, structure of matter (not classified at a more specific level)

83-XX Relativity and gravitational theory

• 83-99 Relativity (not classified at a more specific level)

85-XX Astronomy and astrophysics [For celestial mechanics, see 70F15]

• 85-99 Astronomy and astrophysics (not classified at a more specific level)

86-XX Geophysics [See also 76U05, 76V05]

• 86-99 Geophysics (not classified at a more specific level)

90-XX Operations research, mathematical programming

• 90-99 Operations research, programming (not classified at a more specific level)

91-XX Game theory, economics, social and behavioral sciences

• 91-99 Game theory, economics, social and behavioral sciences (not classified at a more specific level)
• 91A40 Game-theoretic models [Nouveau code MSC 2000]
  • Code MSC1991 affilié : 90D40

92-XX Biology and other natural sciences

• 92-99 Biology and other natural sciences (not classified at a more specific level)
• 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

93-XX Systems theory; control [For optimal control, see 49-XX]

• 93-99 Systems theory; control (not classified at a more specific level)
• 93B28 Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]

94-XX Information and communication, circuits

• 94-99 Information and communication, circuits (not classified at a more specific level)
• 94A24 Coding theorems (Shannon theory)

97-XX Mathematics education

• 97-99 Mathematics education (not classified at a more specific level)
• 97C50 Theoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.) [See also 97D20]
• 97D20 Philosophical and theoretical contributions to mathematical education [See also 97C50]

---

Mot-clé :

---

Retour à la page Classification Mathématique par Matières (version 2000)