- class existence theorem
- теорема существования классов
English-Russian scientific dictionary. 2008.
class existence theorem
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Takagi existence theorem — In class field theory, the Takagi existence theorem states that for any number field K there is a one to one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K ) and the generalized… … Wikipedia
Class formation — In mathematics, a class formation is a structure used to organize the various Galois groups and modules that appear in class field theory. They were invented by Emil Artin and John Tate. Contents 1 Definitions 2 Examples of class formations 3 The … Wikipedia
Class field theory — In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of number fields. Most of the central results in this area were proved in the period between 1900 and 1950. The theory takes its name… … Wikipedia
Class (set theory) — In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) which can be unambiguously defined by a property that all its members share. The precise definition of class… … Wikipedia
Class number problem — In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields with class number n. It is named after the great… … Wikipedia
Theorem — The Pythagorean theorem has at least 370 known proofs[1] In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements … Wikipedia
Nash embedding theorem — The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance,… … Wikipedia
Spectral theorem — In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a … Wikipedia
Löwenheim–Skolem theorem — In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… … Wikipedia
Frobenius theorem (differential topology) — In mathematics, Frobenius theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first order homogeneous linear partial differential equations. In modern geometric terms … Wikipedia
Isomorphism theorem — In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules,… … Wikipedia
