ACTA issues

Expansions of minimal varieties

Ágnes Szendrei

Acta Sci. Math. (Szeged) 60:3-4(1995), 659-679

Abstract. Let $\bf A$ be a strictly simple algebra generating a locally finite minimal variety, and let us expand $\bf A$ arbitrarily with new operations to get an algebra ${\bf A}^\bullet $. We investigate the question under what conditions ${\bf A}^\bullet $ generates a minimal variety. Our result shows that if the tame congruence theoretic type label of $\bf A$ is distinct from 5 or if $\bf A$ has a trivial automorphism group, then ${\bf A}^\bullet $ generates a minimal variety if and only if ${\bf A}^\bullet $ is nonabelian or has a trivial subalgebra.

AMS Subject Classification (1991): 08B05, 08A05, 08A40

Received October 25, 1994, and in revised form January 17, 1995. (Registered under 5657/2009.)