publication . Article . Preprint . 2013

minimal quasivarieties of semilattices over commutative groups

Nagy, Ildikó V.;
Open Access
  • Published: 26 Sep 2013 Journal: Algebra universalis, volume 70, pages 309-325 (issn: 0002-5240, eissn: 1420-8911, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
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.
Subjects
arXiv: Mathematics::LogicMathematics::General MathematicsMathematics::Rings and AlgebrasMathematics::General Topology
free text keywords: Algebra and Number Theory, Automorphism, Algebra, Commutative property, Mathematics, Discrete mathematics, Semilattice, Abelian group, Zero element, Unary operation, Mathematics - Rings and Algebras, 06A12

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