# Definition:Module Automorphism

## Definition

Let $\left({G, +_G, \circ}\right)_R$ 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.