\begin{definition}[Definition:Ring Epimorphism]
Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.
Let $\phi: R \to S$ be a (ring) homomorphism.
Then $\phi$ is a ring epimorphism {{iff}} $\phi$ is a surjection.
\end{definition}