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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 K, it is a function F : A → B {\displaystyle F\colon A\to B} such that for all k in K and x, y in A,
The first two conditions say that F is a K-linear map , and the last condition says that F is a 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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