# Definition:Field Automorphism

## Definition

Let $\struct {F, +, \circ}$ be a field.

Let $\phi: F \to F$ be a (field) isomorphism from $F$ to itself.

Then $\phi$ is a field 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.