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