# Definition:Field Epimorphism

## Definition

Let $\left({F, +, \circ}\right)$ and $\left({K, \oplus, *}\right)$ be fields.

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

Then $\phi$ is a field epimorphism if and only if $\phi$ is a surjection.

## Linguistic Note

The word epimorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix epi- meaning onto.

Thus epimorphism means onto (similar) structure.