Definition:Unital Ring Homomorphism

Definition
Let $R$ and $S$ be rings with unities $1_R$ and $1_S$ respectively.

A unital ring homomorphism is a ring homomorphism $f: R \to S$ such that $\map f {1_R} = 1_S$.

Also see

 * Unity of Ring is Unique
 * Ring Homomorphism Preserves Zero
 * Ring Epimorphism Preserves Unity