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Generators and relations for subsemigroups via boundaries in Cayley graphs

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dc.contributor.authorGray, R
dc.contributor.authorRuskuc, Nik
dc.date.accessioned2011-12-23T11:08:36Z
dc.date.available2011-12-23T11:08:36Z
dc.date.issued2011-11
dc.identifier5158279
dc.identifierab2695c1-8bc5-44a7-9e4f-a46efd512876
dc.identifier79956008214
dc.identifier.citationGray , R & Ruskuc , N 2011 , ' Generators and relations for subsemigroups via boundaries in Cayley graphs ' , Journal of Pure and Applied Algebra , vol. 215 , no. 11 , pp. 2761-2779 . https://doi.org/10.1016/j.jpaa.2011.03.017en
dc.identifier.issn0022-4049
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702072
dc.identifier.urihttps://hdl.handle.net/10023/2131
dc.description.abstractGiven a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T has a finite boundary in S then T is finitely presented. Several corollaries and examples are given.
dc.format.extent490278
dc.language.isoeng
dc.relation.ispartofJournal of Pure and Applied Algebraen
dc.rightsThis is an author version of this article. The definitive version (c) 2011 Elsevier B.V. is available from www.sciencedirect.comen
dc.subjectSemigroupen
dc.subjectGeneratorsen
dc.subjectPresentationsen
dc.subjectCayley graphen
dc.subjectSubsemigroupen
dc.subjectReidemeister-Schreier rewritingen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleGenerators and relations for subsemigroups via boundaries in Cayley graphsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorEPSRCen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1016/j.jpaa.2011.03.017
dc.description.statusPeer revieweden
dc.identifier.grantnumberEP/C523229/1en
dc.identifier.grantnumberEP/E043194/1en
dc.identifier.grantnumberEP/H011978/1en


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