Abstract
We continue some recent investigations of W. Dziobiak, J. Ježek, and M. Maróti. Let \({{\bf G} = {\langle G, \cdot \rangle}}\) 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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Presented by E. Kiss.
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Nagy, I.V. Minimal quasivarieties of semilattices over commutative groups. Algebra Univers. 70, 309–325 (2013). https://doi.org/10.1007/s00012-013-0255-y
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DOI: https://doi.org/10.1007/s00012-013-0255-y