Left strongly Archimedean ordered semigroups.
type: Item
instance of: scholarly article
title: Left strongly Archimedean ordered semigroups.
zbMATH Open document ID: 1342.06008
author: Niovi Kehayopulu
author: Michael Tsingelis
published in: Semigroup Forum
publication date: 2016-02-01T00:00:00Z
review text: As we know, a semigroup (without order) is left strongly Archimedean if and only if it is a nil extension of a left strongly simple semigroup [\textit{M. S. Mitrović}, Semilattices of Archimedean semigroups. Niš: University of Niš, Faculty of Mechanical Engineering (2003; Zbl 1086.20033)]. It is interesting to know what is the matter in case of ordered semigroups. In this note the authors first give a characterization of left strongly Archimedean ordered semigroups. Using this characterization the authors prove that if an ordered semigroup is a nil extension of a left strongly simple ordered semigroup, then it is left strongly Archimedean, and the authors give an example which shows that the converse statement does not hold in general. This reveals a difference between semigroups and ordered semigroups. However, if an ordered semigroup is left strongly Archimedean, then it is a nil extension of a simple ordered semigroup.
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 6537654
zbMATH Keywords: Archimedean ordered semigroups
zbMATH Keywords: left quasi \(\pi\)-regular semigroups
zbMATH Keywords: intra \(\pi\)-regular semigroups
zbMATH Keywords: left strongly Archimedean semigroups
zbMATH Keywords: left strongly simple semigroups
zbMATH Keywords: nil extensions
reviewed by: Xie Xiang-Yun
MaRDI profile type: Publication
full work available at URL: s00233-014-9672-2
OpenAlex ID: W1990388226
cites work: Nil-extensions of simple po-semigroups
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cites work: Ideal Extensions of Ordered Semigroups
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cites work: Ordered semigroups in which the left ideals are intra-regular semigroups
cites work: On Ordered Semigroups Which are Semilattices of Simple and Regular Semigroups
cites work: Q4821971
DOI: 10.1007/S00233-014-9672-2
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description: scientific article; zbMATH DE number 6537654