Minimal quasivarieties of semilattices over commutative groups

摘要

We continue some recent investigations of W. Dziobiak, J. Je?ek, and M. Maróti. Let G = 〈G,□〉 be a commutative group. A semilattice over G is a semilattice enriched with G as a set of unary operations acting as semilattice automorphisms. We prove that the minimal quasivarieties of semilattices over a finite abelian group G are in one-to-one correspondence with the subgroups of G. If G is not finite, then we reduce the description of minimal quasivarieties to that of those minimal quasivarieties in which not every algebra has a zero element.