Definition:Field Epimorphism
Jump to navigation
Jump to search
Definition
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 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.