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dc.contributor.authorMiller, Craig
dc.contributor.authorRuskuc, Nikola
dc.date.accessioned2020-01-27T00:34:44Z
dc.date.available2020-01-27T00:34:44Z
dc.date.issued2019-01-27
dc.identifier.citationMiller , C & Ruskuc , N 2019 , ' An introduction to presentations of monoid acts : quotients and subacts ' , Communications in Algebra , vol. Latest Articles . https://doi.org/10.1080/00927872.2018.1498862en
dc.identifier.issn0092-7872
dc.identifier.otherPURE: 253280045
dc.identifier.otherPURE UUID: 8ff6b47c-70a8-4568-b081-c4eaa5faab9c
dc.identifier.otherScopus: 85060818955
dc.identifier.otherWOS: 000463799700026
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702026
dc.identifier.urihttps://hdl.handle.net/10023/19357
dc.description.abstractThe purpose of this paper is to introduce the theory of presentations of monoids acts. We aim to construct ‘nice’ general presentations for various act constructions pertaining to subacts and Rees quotients. More precisely, given an M-act A and a subact B of A, on the one hand we construct presentations for Band the Rees quotient A/B using a presentation for A, and on the other hand we derive a presentation for A from presentations for B and A/B. We also construct a general presentation for the union of two subacts. From our general presentations, we deduce a number of finite presentability results. Finally, we consider the case where a subact B has finite complement in an M-act A. Weshow that if M is a finitely generated monoid and B is finitely presented, then A is finitely presented. We also show that if M belongs to a wide class of monoids, including all finitely presented monoids, then the converse also holds.
dc.language.isoeng
dc.relation.ispartofCommunications in Algebraen
dc.rights© 2018, Taylor & Francis Group, LLC. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1080/00927872.2018.1498862en
dc.subjectMonoid acten
dc.subjectPresentationen
dc.subjectSubacten
dc.subjectRees quotienten
dc.subjectUnionen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleAn introduction to presentations of monoid acts : quotients and subactsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.identifier.doihttps://doi.org/10.1080/00927872.2018.1498862
dc.description.statusPeer revieweden
dc.date.embargoedUntil2020-01-27
dc.identifier.urlhttps://arxiv.org/abs/1709.08916en


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