Definition:Module Automorphism

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Let $\struct {G, +_G, \circ}_R$ be an $R$-module.

Let $\phi: G \to G$ be a module isomorphism to itself.

Then $\phi$ is a module automorphism.

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.

Also see