Abstract
A finite algebra is called automorphism-primal if its clone of term operations coincides with all operations that preserve its automorphisms. We prove that the variety generated by an automorphism-primal algebra is verbose, that is, on every member algebra, every fully invariant congruence is verbal. The proof is a nice application of the theory of natural dualities as developed by Davey et al.
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Presented by R. Quackenbush.
For Brian Davey on the occasion of his 65th birthday.
Research partially supported by the Barbara J. Janson professorship.
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Bergman, C. Automorphism-primal algebras generate verbose varieties. Algebra Univers. 74, 117–122 (2015). https://doi.org/10.1007/s00012-015-0337-0
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DOI: https://doi.org/10.1007/s00012-015-0337-0