Definition:Algebra Homomorphism

Definition
Let $R$ be a commutative ring.

Let $\struct {A, *}$ and $\struct {B, \times}$ be algebras over $R$.

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

Also see

 * Definition:Unital Algebra Homomorphism