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
Suppose is a variety of algebras, and is an algebra in . An I-automorphism of is an automorphism that can be expressed as:
where are fixed, and is a word in terms of the operations of the algebra,with the property that for any algebra of , and any choice of values , the map:
gives an automorphism of .
In other words is guaranteed to give an automorphism.
In the variety of groups, the I-automorphisms are precisely the inner automorphisms: the automorphisms of the form . For full proof, refer: Inner automorphisms are I-automorphisms in variety of groups