Definition:Semigroup Epimorphism

Definition

Let $\struct {S, \circ}$ and $\struct {T, *}$ be semigroups.

Let $\phi: S \to T$ be a (semigroup) homomorphism.

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

Also see

• Results about semigroup epimorphisms can be found here.

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

• 1974: Thomas W. Hungerford: Algebra ... (previous) ... (next): $\S 1.2$: Definition $2.1$