Definition:Ring Automorphism

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Let $\struct {R, +, \circ}$ be a ring.

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

Then $\phi$ is a ring automorphism.

That is, a ring automorphism is a (ring) isomorphism from a ring to itself.

Also see

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.