Definition:Unital Algebra Homomorphism

Definition
Let $R$ be a commutative ring.

Let $\struct {A, *}$ and $\struct {B, \times}$ be unital algebras over $R$ with units $1_A$ and $1_B$.

A unital algebra homomorphism $f : A \to B$ is a algebra homomorphism such that $\map f {1_A} = 1_B$.