J Austral Math Soc Ser A 48 pp434--454, 1990.

Simple Surjective Algebras Having No Proper Subalgebras

Ágnes Szendrei

Abstract

We prove that every finite, simple, surjective algebra having no proper subalgebras is either quasiprimal or affine or isomorphic to an algebra term equivalent to a matrix power of a unary permutational algebra. Consequently, it generates a minimal variety if and only if it is quasiprimal. We show also that a locally finite, minimal variety omitting type 1 is minimal as a quasivariety if and only if it has a unique subdirectly irreducible algebra.

1980 AMS Subject Classification (1985 Revision): 08A05, 08A40, 08B05

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Authors

Ágnes Szendrei

Bolyai Institute, Aradi vértanúk tere 1, 6720 Szeged, Hungary.