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dc.contributor.authorMaltcev, V.
dc.contributor.authorMitchell, J. D.
dc.contributor.authorRuskuc, N.
dc.date.accessioned2012-01-04T12:11:51Z
dc.date.available2012-01-04T12:11:51Z
dc.date.issued2009-08
dc.identifier.citationMaltcev , V , Mitchell , J D & Ruskuc , N 2009 , ' The Bergman property for semigroups ' , Journal of the London Mathematical Society , vol. 80 , no. 1 , pp. 212-232 . https://doi.org/10.1112/jlms/jdp025en
dc.identifier.issn0024-6107
dc.identifier.otherPURE: 2338162
dc.identifier.otherPURE UUID: 97f7e0f8-4128-4ca7-9b45-9aa1a53ca2d0
dc.identifier.otherWOS: 000268112000013
dc.identifier.otherScopus: 68349128462
dc.identifier.otherORCID: /0000-0002-5489-1617/work/73700785
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702027
dc.identifier.urihttp://hdl.handle.net/10023/2145
dc.description.abstractIn this article, we study the Bergman property for semigroups and the associated notions of cofinality and strong cofinality. A large part of the paper is devoted to determining when the Bergman property, and the values of the cofinality and strong cofinality, can be passed from semigroups to subsemigroups and vice versa. Numerous examples, including many important semigroups from the literature, are given throughout the paper. For example, it is shown that the semigroup of all mappings on an infinite set has the Bergman property but that its finitary power semigroup does not; the symmetric inverse semigroup on an infinite set and its finitary power semigroup have the Bergman property; the Baer-Levi semigroup does not have the Bergman property.
dc.format.extent21
dc.language.isoeng
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.rightsThis is an author version of this article. The published version, (c) 2009 London Mathematical Society, is available from Oxford Journals at doi: 10.1112/jlms/jdp025en
dc.subjectFinitary power semigroupsen
dc.subjectGenerating countable setsen
dc.subjectUncountable cofinalitiesen
dc.subjectInfiniteen
dc.subjectTransformationsen
dc.subjectEndomorphismsen
dc.subjectMonoidsen
dc.subjectRanksen
dc.subjectQA Mathematicsen
dc.subject.lccQAen
dc.titleThe Bergman property for semigroupsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1112/jlms/jdp025
dc.description.statusPeer revieweden
dc.identifier.urlhttp://www.scopus.com/inward/record.url?scp=68349128462&partnerID=8YFLogxKen


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