About: Algebra homomorphism

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In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if A and B are algebras over a field (or commutative ring) K, it is a function such that for all k in K and x, y in A, * * * The first two conditions say that F is a K-linear map (or K-module homomorphism if K is a commutative ring), and the last condition says that F is a (non-unital) ring homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B.

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  • In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if A and B are algebras over a field (or commutative ring) K, it is a function such that for all k in K and x, y in A, * * * The first two conditions say that F is a K-linear map (or K-module homomorphism if K is a commutative ring), and the last condition says that F is a (non-unital) ring homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B. (en)
  • Un omomorfismo tra due algebre sul campo K, A e B, è una funzione tale che per ogni k in K e x,y in A, * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) Se F è biettiva allora F è detta isomorfismo tra A e B. (it)
  • 在A和B兩個K-多元環之間的同態是指一個函數，此函數能使得對所有在K內的k和在A內的x、y來說， * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) 若F是双射的，則F稱為是A和B之間的同構。 (zh)
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  • In mathematics, an algebra homomorphism is a homomorphism between two associative algebras. More precisely, if A and B are algebras over a field (or commutative ring) K, it is a function such that for all k in K and x, y in A, * * * The first two conditions say that F is a K-linear map (or K-module homomorphism if K is a commutative ring), and the last condition says that F is a (non-unital) ring homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B. (en)
  • Un omomorfismo tra due algebre sul campo K, A e B, è una funzione tale che per ogni k in K e x,y in A, * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) Se F è biettiva allora F è detta isomorfismo tra A e B. (it)
  • 在A和B兩個K-多元環之間的同態是指一個函數，此函數能使得對所有在K內的k和在A內的x、y來說， * F(kx) = kF(x) * F(x + y) = F(x) + F(y) * F(xy) = F(x)F(y) 若F是双射的，則F稱為是A和B之間的同構。 (zh)
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  • Algebra homomorphism (en)
  • Omomorfismo di algebre (it)
  • 代數同態 (zh)
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