Definition:Ring Epimorphism

Definition
Let $\left({R, +, \circ}\right)$ and $\left({S, \oplus, *}\right)$ be rings.

Let $\phi: R \to S$ be a (ring) homomorphism.

Then $\phi$ is a ring epimorphism iff $\phi$ is a surjection.

Also see

 * Epimorphism