# Strong formula automorphism

From Groupprops

This article defines a property that can be evaluated for an automorphism of an algebra in a variety of algebras. The evaluation of that property depends on the ambient variety, and not just on the automorphism or the algebra.

View all such properties

## Contents

## Definition

An automorphism of an algebra in a variety of algebras is a formula automorphism whose inverse is also a formula automorphism.

## Particular cases

### For groups

Strong formula automorphisms in the case of groups are called strong monomial automorphisms.

## Relation with other properties

### Stronger properties

- I-automorphism:
`For full proof, refer: I-automorphism implies strong formula automorphism`