Minimal varieties and quasivarieties

Clifford Bergman, Ralph McKenzie
1990 Journal of the Australian Mathematical Society  
We prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. 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 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 08 B 15, 08 C
more » ... ion): 08 B 15, 08 C 15, 08 B 10, 03 G 25, 08 A 40.
doi:10.1017/s1446788700035266 fatcat:ejxakzfbrzhb3nljv3uvyfdaiq