Bergman, Clifford Automorphism-primal algebras generate verbose varieties. (English) Zbl 1323.08005 Algebra Univers. 74, No. 1-2, 117-122 (2015). A finite algebra is automorphism-primal if its clone of term functions coincides with the clone of all operations that preserve its automorphisms. It was proved by H. Werner that a finite algebra is automorphism-primal if and only if it is quasiprimal, every subuniverse is the set of fixed points of a group of automorphisms, and every isomorphism between nontrivial subalgebras can be extended to an automorphism of the whole algebra. As an example, every finite field is automorphism-primal. It is proved that the variety generated by an automorphism-primal algebra is verbose, i.e. that every fully invariant congruence on each of its members is verbal. The proof use natural dualities as developed by B. Davey. Reviewer: Ivan Chajda (Přerov) MSC: 08B10 Congruence modularity, congruence distributivity 08A30 Subalgebras, congruence relations 08A35 Automorphisms and endomorphisms of algebraic structures 08C20 Natural dualities for classes of algebras Keywords:finite algebras; verbal congruences; fully invariant congruences; automorphism-primal algebras; natural dualities; verbose algebras; verbose varieties PDFBibTeX XMLCite \textit{C. Bergman}, Algebra Univers. 74, No. 1--2, 117--122 (2015; Zbl 1323.08005) Full Text: DOI Link References: [1] Bergman, C.: Universal Algebra. Fundamentals and Selected Topics, Pure and Applied Mathematics (Boca Raton), vol. 301. CRC Press, Boca Raton, FL (2012) · Zbl 1229.08001 [2] Bergman C., Berman J.: Fully invariant and verbal congruence relations. Algebra Universalis 70, 71-94 (2013) · Zbl 1280.08001 · doi:10.1007/s00012-013-0238-z [3] Clark, D.M., Davey, B.A.: Natural Dualities for the Working Algebraist, Cambridge Studies in Advanced Mathematics, vol. 57. Cambridge University Press, Cambridge (1998) · Zbl 0910.08001 [4] Werner, H.: Discriminator Algebras. Studium zur Algebra und ihre Andwendungen 6. Akademie Verlag, Berlin (1978) · Zbl 1280.08001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.