Variety-infinity-extensible automorphism

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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.
View all such properties

Definition

Let ${\mathcal {V}}$ be a variety of algebras, and $A$ be an algebra in ${\mathcal {V}}$. An automorphism $\sigma$ of $A$ is termed infinity-extensible over the variety ${\mathcal {V}}$ if it is $\alpha$-extensible over ${\mathcal {V}}$ for every ordinal $\alpha$.

Relation with other properties

Stronger properties

• I-automorphism
• Variety-infinity-pushforwardable automorphism

Weaker properties

• Variety-chain-extensible automorphism
• Variety-extensible automorphism