On certain lattice-ordered semigroups
type: Item
instance of: scholarly article
title: On certain lattice-ordered semigroups
zbMATH Open document ID: 0565.06013
DOI: 10.1007/BF02572663
author: Gabriel Ciobanu
author: Marian Deaconescu
published in: Semigroup Forum
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134760
review text: The aim of this paper is the introduction and the initial study of a lattice-ordered semigroup S which satisfies \(ab=(a\vee b)(a\wedge b)\) for all a,b\(\in S\). This axiom is of course a well-known theorem of the classical theory of divisibility over commutative and cancellative semigroups. Furthermore, the paper establishes some connections between the subjacent lattice and semigroup structures of such a lattice-ordered semigroup which the authors have called arithmetical lattice-semigroup (shortly: a.l.-semigroup). The reason why the authors chose this name was mainly suggested by both the fact that N is such an a.l.-semigroup and the decomposition theorem given in this paper.
reviewed by: Richard A. Aló
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 3900830
zbMATH Keywords: lattice-ordered semigroup
zbMATH Keywords: cancellative semigroups
zbMATH Keywords: arithmetical lattice- semigroup
zbMATH Keywords: decomposition theorem
Wikidata QID: Q57937491
MaRDI profile type: Publication
cites work: Q5820602
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description: scientific article; zbMATH DE number 3900830