Definition:Field Epimorphism
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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.