I-automorphism

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

Definition

Suppose $\mathcal{V}$ is a variety of algebras, and $A$ is an algebra in $\mathcal{V}$. An I-automorphism of $A$ is an automorphism that can be expressed as:

$x\mapsto \phi (x,t_1,t_2,\dots ,t_n)$

where $\phi$ is a word in terms of the operations of the algebra, with the property that for any algebra of $\mathcal{V}$, a map of the above form yields an automorphism.

Relation with other properties

Weaker properties

• Formula automorphism
• Variety-extensible automorphism