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arXiv · 1208.5579

Minimal quasivarieties of semilattices over commutative groups

Ildikó V. Nagy
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Abstract

We continue some recent investigations of W. Dziobiak, J. Jezek, and M. Maroti. Let G=(G,\cdot) 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.

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Ildikó V. Nagy. 2012-08-28. Minimal quasivarieties of semilattices over commutative groups. https://arxiv.org/abs/1208.5579

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