# Definition:Ring Monomorphism

## Definition

Let $\struct {R, +, \circ}$ and $\struct {S, \oplus, *}$ be rings.

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

Then $\phi$ is a ring monomorphism if and only if $\phi$ is an injection.

## Also known as

A monomorphism may also be referred to as an embedding.

## Linguistic Note

The word monomorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix mono- meaning single.

Thus monomorphism means single (similar) structure.