\begin{definition}[Definition:Algebra Homomorphism]
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:
:$\forall a, b \in A : f(a * b) = f(a) \times f(b)$
\end{definition}