J Austral Math Soc Ser A 48 pp133--147, 1990.

Minimal Varieties and Quasivarieties

Clifford Bergman and Ralph McKenzie

Abstract

We prove that every locally finite, congruence modular, minimal variety is minimal as a quasi-variety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the set of unary term operations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.

1980 AMS Subject Classification (1985 Revision): 08B15, 08C15, 08B10, 03G25, 08A40

Browse the article

Authors

Clifford Bergman

Iowa State Unievrsity, Ames, Iowa 50011, U.S.A.

Ralph McKenzie

University of California, Berkeley, California 94720, U.S.A.