Algebra homomorphism

A homomorphism between two associative algebras, A and B, over a field (or commutative ring) K, is a function F : A → B {displaystyle Fcolon A o B} such that for all k in K and x, y in A, A homomorphism between two associative algebras, A and B, over a field (or commutative ring) K, is a function F : A → B {displaystyle Fcolon A o B} such that for all k in K and x, y in A, The first two conditions say that F is a K-module homomorphism between K-modules. If F admits an inverse homomorphism or equivalently if it is bijective, F is said to be an isomorphism from A to B.