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Automatic presentations and semigroup constructions
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dc.contributor.author | Cain, Alan J. | |
dc.contributor.author | Oliver, Graham | |
dc.contributor.author | Ruskuc, Nik | |
dc.contributor.author | Thomas, Richard M. | |
dc.date.accessioned | 2012-01-04T12:41:54Z | |
dc.date.available | 2012-01-04T12:41:54Z | |
dc.date.issued | 2010-08 | |
dc.identifier.citation | Cain , A J , Oliver , G , Ruskuc , N & Thomas , R M 2010 , ' Automatic presentations and semigroup constructions ' , Theory of Computing Systems , vol. 47 , no. 2 , pp. 568-592 . https://doi.org/10.1007/s00224-009-9216-4 | en |
dc.identifier.issn | 1432-4350 | |
dc.identifier.other | PURE: 2338306 | |
dc.identifier.other | PURE UUID: 011e98ad-56c8-48d1-8b0e-ab3a4e91d28f | |
dc.identifier.other | WOS: 000278029300011 | |
dc.identifier.other | Scopus: 77952952975 | |
dc.identifier.other | ORCID: /0000-0003-2415-9334/work/73702061 | |
dc.identifier.uri | https://hdl.handle.net/10023/2148 | |
dc.description.abstract | An automatic presentation for a relational structure is, informally, an abstract representation of the elements of that structure by means of a regular language such that the relations can all be recognized by finite automata. A structure admitting an automatic presentation is said to be FA-presentable. This paper studies the interaction of automatic presentations and certain semigroup constructions, namely: direct products, free products, finite Rees index extensions and subsemigroups, strong semilattices of semigroups, Rees matrix semigroups, Bruck-Reilly extensions, zero-direct unions, semidirect products, wreath products, ideals, and quotient semigroups. For each case, the closure of the class of FA-presentable semigroups under that construction is considered, as is the question of whether the FA-presentability of the semigroup obtained from such a construction implies the FA-presentability of the original semigroup[s]. Classifications are also given of the FA-presentable finitely generated Clifford semigroups, completely simple semigroups, and completely 0-simple semigroups. | |
dc.format.extent | 25 | |
dc.language.iso | eng | |
dc.relation.ispartof | Theory of Computing Systems | en |
dc.rights | This is an author version of this article. The original publication, (c) Springer Science+Business Media, LLC 2009, is available at www.springerlink.com | en |
dc.subject | Automatic presentation | en |
dc.subject | FA-presentable | en |
dc.subject | Semigroup construction | en |
dc.subject | Clifford semigroup | en |
dc.subject | Completely simple semigroup | en |
dc.subject | Subsemigroups | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | Automatic presentations and semigroup constructions | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | 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/10.1007/s00224-009-9216-4 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=77952952975&partnerID=8YFLogxK | en |
dc.identifier.grantnumber | EP/C523229/1 | en |
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