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Green index and finiteness conditions for semigroups
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dc.contributor.author | Gray, Robert Duncan | |
dc.contributor.author | Ruskuc, Nik | |
dc.date.accessioned | 2012-01-04T12:11:47Z | |
dc.date.available | 2012-01-04T12:11:47Z | |
dc.date.issued | 2008-10-15 | |
dc.identifier.citation | Gray , R D & Ruskuc , N 2008 , ' Green index and finiteness conditions for semigroups ' , Journal of Algebra , vol. 320 , no. 8 , pp. 3145-3164 . https://doi.org/10.1016/j.jalgebra.2008.07.008 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | PURE: 600778 | |
dc.identifier.other | PURE UUID: 87b2d1e8-d2f3-4d7b-a516-ad808850fe54 | |
dc.identifier.other | WOS: 000259715600006 | |
dc.identifier.other | Scopus: 51249099150 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/73702062 | |
dc.identifier.uri | https://hdl.handle.net/10023/2144 | |
dc.description.abstract | Let S be a semigroup and let T be a subsemigroup of S. Then T acts on S by left and by right multiplication. If the complement S \ T has finitely many strong orbits by both these actions we say that T has finite Green index in S. This notion of finite index encompasses subgroups of finite index in groups, and also subsemigroups of finite Rees index (complement). Therefore, the question of S and T inheriting various finiteness conditions from each other arises. In this paper we consider and resolve this question for the following finiteness conditions: finiteness, residual finiteness, local finiteness, periodicity, having finitely many right ideals, and having finitely many idempotents. (c) 2008 Elsevier Inc. All rights reserved. | |
dc.format.extent | 20 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.rights | This is an author version of this article. The published version (c) 2008 Elsevier Inc. is available at www.sciencedirect.com | en |
dc.subject | Finiteness conditions | en |
dc.subject | Index | en |
dc.subject | Residual finiteness | en |
dc.subject | Local finiteness | en |
dc.subject | Complete rewriting-systems | en |
dc.subject | Subsemigroups | en |
dc.subject | Subgroups | en |
dc.subject | Monoids | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Green index and finiteness conditions for semigroups | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | EPSRC | en |
dc.description.version | Postprint | 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/10.1016/j.jalgebra.2008.07.008 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=51249099150&partnerID=8YFLogxK | en |
dc.identifier.grantnumber | EP/C523229/1 | en |
dc.identifier.grantnumber | EP/E043194/1 | en |
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