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On residual finiteness of direct products of algebraic systems

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dc.contributor.authorGray, R.
dc.contributor.authorRuskuc, Nik
dc.date.accessioned2012-01-04T12:41:47Z
dc.date.available2012-01-04T12:41:47Z
dc.date.issued2009-09
dc.identifier.citationGray , R & Ruskuc , N 2009 , ' On residual finiteness of direct products of algebraic systems ' , Monatshefte für Mathematik , vol. 158 , no. 1 , pp. 63-69 . https://doi.org/10.1007/s00605-008-0036-4en
dc.identifier.issn0026-9255
dc.identifier.otherPURE: 2338206
dc.identifier.otherPURE UUID: 479d696f-a963-4947-88eb-ad3d8b598905
dc.identifier.otherWOS: 000268432300004
dc.identifier.otherScopus: 70349919795
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702043
dc.identifier.urihttp://hdl.handle.net/10023/2146
dc.description.abstractIt is well known that if two algebraic structures A and B are residually finite then so is their direct product. Here we discuss the converse of this statement. It is of course true if A and B contain idempotents, which covers the case of groups, rings, etc. We prove that the converse also holds for semigroups even though they need not have idempotents. We also exhibit three examples which show that the converse does not hold in general.
dc.format.extent7
dc.language.isoeng
dc.relation.ispartofMonatshefte für Mathematiken
dc.rightsThis is an author version of this article. The original publication (c) Springer-Verlag 2008 is available at www.springerlink.comen
dc.subjectResidual finitenessen
dc.subjectDirect producten
dc.subjectSemigroupen
dc.subjectUnary algebraen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleOn residual finiteness of direct products of algebraic systemsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorEPSRCen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1007/s00605-008-0036-4
dc.description.statusPeer revieweden
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=70349919795&partnerID=8YFLogxKen
dc.identifier.grantnumberEP/C523229/1en
dc.identifier.grantnumberEP/E043194/1en


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