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On separability finiteness conditions in semigroups
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dc.contributor.author | Miller, Craig | |
dc.contributor.author | O'Reilly, Gerard | |
dc.contributor.author | Quick, Martyn | |
dc.contributor.author | Ruskuc, Nik | |
dc.date.accessioned | 2021-09-29T15:30:01Z | |
dc.date.available | 2021-09-29T15:30:01Z | |
dc.date.issued | 2022-12 | |
dc.identifier.citation | Miller , C , O'Reilly , G , Quick , M & Ruskuc , N 2022 , ' On separability finiteness conditions in semigroups ' , Journal of the Australian Mathematical Society , vol. 113 , no. 3 , pp. 402-430 . https://doi.org/10.1017/S1446788721000124 | en |
dc.identifier.issn | 1446-7887 | |
dc.identifier.other | PURE: 268621654 | |
dc.identifier.other | PURE UUID: 0d07e2d6-395a-4379-bfd9-9ad21445be78 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/2006.08499v1 | |
dc.identifier.other | ORCID: /0000-0002-5227-2994/work/100900880 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/100901196 | |
dc.identifier.other | Scopus: 85114989744 | |
dc.identifier.other | WOS: 000780241900001 | |
dc.identifier.uri | http://hdl.handle.net/10023/24053 | |
dc.description | Funding: The first author is grateful to EPSRC for financial support. The second author is grateful to the School of Mathematics and Statistics of the University of St Andrews for financial support. | en |
dc.description.abstract | Taking residual finiteness as a starting point, we consider three related finiteness properties: weak subsemigroup separability, strong subsemigroup separability and complete separability. We investigate whether each of these properties is inherited by Schützenberger groups. The main result of this paper states that for a finitely generated commutative semigroup S, these three separability conditions coincide and are equivalent to every H -class of S being finite. We also provide examples to show that these properties in general differ for commutative semigroups and finitely generated semigroups. For a semigroup with finitely many H -classes, we investigate whether it has one of these properties if and only if all its Schützenberger groups have the property. | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of the Australian Mathematical Society | en |
dc.rights | Copyright © Australian Mathematical Publishing Association Inc. 2021. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited | en |
dc.subject | Separability | en |
dc.subject | Finiteness condition | en |
dc.subject | Semigroup | en |
dc.subject | Congruence | en |
dc.subject | Residual finiteness | en |
dc.subject | Commutative semigroup | en |
dc.subject | Schützenberger group | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On separability finiteness conditions in semigroups | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1017/S1446788721000124 | |
dc.description.status | Peer reviewed | en |
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