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  In mathematics, an algebra homomorphism is an 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,
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* The first two conditions say that F is a module homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B.
 In mathematics, an algebra homomorphism is an 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 Klinear map (or Kmodule homomorphism if K is a commutative ring), and the last condition says that F is a (nonunital) 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.
 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 Klinear map (or Kmodule homomorphism if K is a commutative ring), and the last condition says that F is a (nonunital) 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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has abstract
  In mathematics, an algebra homomorphism is an 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 module homomorphism. If F admits an inverse homomorphism, or equivalently if it is bijective, F is said to be an isomorphism between A and B.
 In mathematics, an algebra homomorphism is an 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 Klinear map (or Kmodule homomorphism if K is a commutative ring), and the last condition says that F is a (nonunital) 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.
 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 Klinear map (or Kmodule homomorphism if K is a commutative ring), and the last condition says that F is a (nonunital) 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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