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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.
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Let be a variety of algebras and be an algebra in . A formula automorphism is an automorphism of given by:
where is a word (or expression) in the s, using the operations of , and the are elements of .
A strong formula automorphism is a formula automorphism whose inverse is also a formula automorphism.