Definition:Algebra Homomorphism

Definition
Let $R$ be a commutative ring.

Let $(A, *)$ and $(B, \times)$ be algebras over $R$.

An algebra homomorphism $f : A \to B$ is a module homomorphism such that:
 * $\forall a, b \in A : f(a * b) = f(a) \times f(b)$

Also see

 * Definition:Unital Algebra Homomorphism