Definition:Semigroup Endomorphism

Definition

Let $\struct {S, \circ}$ be a semigroups.

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

Then $\phi$ is a semigroup endomorphism.

Also see

• Definition:Endomorphism

• Results about semigroup endomorphisms can be found here.

Linguistic Note

The word endomorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix endo- (from ἔνδον') meaning inner or internal.

Thus endomorphism means internal structure.

Sources

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