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dc.contributor.authorMiller, Craig
dc.contributor.authorO'Reilly, Gerard
dc.contributor.authorQuick, Martyn
dc.contributor.authorRuskuc, Nik
dc.identifier.citationMiller , C , O'Reilly , G , Quick , M & Ruskuc , N 2022 , ' On separability finiteness conditions in semigroups ' , Journal of the Australian Mathematical Society , vol. 113 , no. 3 , pp. 402-430 .
dc.identifier.otherPURE: 268621654
dc.identifier.otherPURE UUID: 0d07e2d6-395a-4379-bfd9-9ad21445be78
dc.identifier.otherORCID: /0000-0002-5227-2994/work/100900880
dc.identifier.otherORCID: /0000-0003-2415-9334/work/100901196
dc.identifier.otherScopus: 85114989744
dc.identifier.otherWOS: 000780241900001
dc.descriptionFunding: The first author is grateful to EPSRC for financial support. The second author is grateful to the School of Mathematics and Statistics of the University of St Andrews for financial support.en
dc.description.abstractTaking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We investigate whether each of these properties is inherited by Schützenberger groups. The main result of this paper states that for a finitely generated commutative semigroup S, these three separability conditions coincide and are equivalent to every H -class of S being finite. We also provide examples to show that these properties in general differ for commutative semigroups and finitely generated semigroups. For a semigroup with finitely many H -classes, we investigate whether it has one of these properties if and only if all its Schützenberger groups have the property.
dc.relation.ispartofJournal of the Australian Mathematical Societyen
dc.rightsCopyright © Australian Mathematical Publishing Association Inc. 2021. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence ( licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly citeden
dc.subjectFiniteness conditionen
dc.subjectResidual finitenessen
dc.subjectCommutative semigroupen
dc.subjectSchützenberger groupen
dc.subjectQA Mathematicsen
dc.titleOn separability finiteness conditions in semigroupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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