Definition:Ring Epimorphism

From ProofWiki
Jump to: navigation, search

Definition

Let $\left({R, +, \circ}\right)$ and $\left({S, \oplus, *}\right)$ be rings.

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


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


Also see


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.


Sources