Minimal varieties and quasivarieties. (English) Zbl 0692.08011
The main result is: If V is a minimal, locally finite and congruence distributive variety then V is a minimal quasivariety. An example of a finite algebra generating a minimal variety which is not a minimal quasivariety is given. The authors construct all finite, strictly simple algebras generating a congruence distributive variety such that the set of unary term operations forms a group. The last section is an application to algebraic logic.
Reviewer: J.Ježek
MSC:
08B15 | Lattices of varieties |
08C15 | Quasivarieties |
03G25 | Other algebras related to logic |
08B10 | Congruence modularity, congruence distributivity |
08A40 | Operations and polynomials in algebraic structures, primal algebras |