Formula automorphism

Definition
Let $$\mathcal{V}$$ be a variety of algebras and $$A$$ be an algebra in $$\mathcal{V}$$. A formula automorphism is an automorphism of $$A$$ given by:

$$x \mapsto f(x, x_2, x_3, \dots, x_n)$$

where $$f$$ is a word (or expression) in the $$x_i$$s, using the operations of $$\mathcal{V}$$, and the $$x_i$$ are elements of $$A$$.

A strong formula automorphism is a formula automorphism whose inverse is also a formula automorphism.

For groups
In the case of groups, the formula automorphisms are called monomial automorphisms. An automorphism such that both that and its inverse are monomial is termed a strong monomial automorphism.

Stronger properties

 * Weaker than::I-automorphism

Weaker properties

 * Stronger than::Weak IC-automorphism