Definition:Ring Automorphism

Definition

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

• Definition:Automorphism (Abstract Algebra)

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

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 3$. Homomorphisms
• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.2$: Homomorphisms: Definition $2.4$