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dc.contributor.authorO'Reilly, Gerard Aidan
dc.contributor.authorQuick, Martyn
dc.contributor.authorRuskuc, Nik
dc.identifier.citationO'Reilly , G A , Quick , M & Ruskuc , N 2021 , ' On separability properties in direct products of semigroups ' , Monatshefte für Mathematik , vol. 197 , no. 2 , pp. 333-352 .
dc.identifier.otherPURE: 274172445
dc.identifier.otherPURE UUID: 8130455d-3ac6-47ad-a7ab-1955361fa936
dc.identifier.otherORCID: /0000-0002-5227-2994/work/94669106
dc.identifier.otherORCID: /0000-0003-2415-9334/work/94669433
dc.identifier.otherScopus: 85106687824
dc.identifier.otherWOS: 000655421000003
dc.description.abstractWe investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup separability. For each of these properties we examine under which conditions the property is preserved under direct products. We also consider if any of the properties are inherited by the factors in a direct product. We give necessary and sufficient conditions for finite semigroups to preserve the properties of strong subsemigroup separability and monogenic subsemigroup separability in a direct product.
dc.relation.ispartofMonatshefte für Mathematiken
dc.rightsCopyright © The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence,and indicate if changes were made. The images or other third party material in this article are includedin the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. Ifmaterial is not included in the article’s Creative Commons licence and your intended use is not permittedby statutory regulation or exceeds the permitted use, you will need to obtain permission directly from thecopyright holder. To view a copy of this licence, visit
dc.subjectResidual propertiesen
dc.subjectSubsemigroup separabilityen
dc.subjectResidual finitenessen
dc.subjectComplete separabilityen
dc.subjectDirect productsen
dc.subjectFinite index congruenceen
dc.subjectQA Mathematicsen
dc.titleOn separability properties in direct products of 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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