Definition:Semigroup Automorphism

Definition

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

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

Then $\phi$ is a semigroup automorphism.

Also see

• Results about semigroup automorphisms can be found here.

Linguistic Note

The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.

Thus automorphism means self structure.

Sources

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