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composition theorem

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  • Composition series — In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many… …   Wikipedia

  • Composition algebra — In mathematics, a composition algebra A over a field K is a unital (but not necessarily associative) algebra over K together with a nondegenerate quadratic form N which satisfies for all x and y in A.  The quadratic form N is often referred… …   Wikipedia

  • Composition operator — For information about the operator ∘ of composition, see function composition and composition of relations. In mathematics, the composition operator Cϕ with symbol ϕ is a linear operator defined by the rule where denotes function composition. In… …   Wikipedia

  • Okishio's theorem — is a mathematical theorem formulated by Japanese economist Nobuo Okishio. It has had a major impact on debates about Marx s theory of value. Intuitively, it can be understood as saying that if one capitalist raises his profits by introducing a… …   Wikipedia

  • Menelaus' theorem — Menelaus theorem, case 1: line DEF passes inside triangle ABC Menelaus theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, and a transversal line that crosses BC, AC and AB at points D …   Wikipedia

  • Hurwitz's theorem — In mathematics, Hurwitz s theorem is any of at least five different results named after Adolf Hurwitz. Hurwitz s theorem in complex analysis In complex analysis, Hurwitz s theorem roughly states that, under certain conditions, if a sequence of… …   Wikipedia

  • Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… …   Wikipedia

  • Cayley's theorem — In group theory, Cayley s theorem, named in honor of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group on G . This can be understood as an example of the group action of G on the elements of G .A… …   Wikipedia

  • Schur–Zassenhaus theorem — The Schur–Zassenhaus theorem is a theorem in group theory which states that if G is a finite group, and N is a normal subgroup whose order is coprime to the order of the quotient group G/N, then G is a semidirect product of N and G/N.An… …   Wikipedia

  • Kleene's recursion theorem — In computability theory, Kleene s recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first proved by Stephen Kleene in 1938.This article uses the… …   Wikipedia

  • Stinespring factorization theorem — In mathematics, Stinespring s dilation theorem, also called Stinespring s factorization theorem, is a result from operator theory that represents any completely positive map on a C* algebra as a composition of two completely positive maps each of …   Wikipedia

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