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dc.contributor.authorCain, Alan J.
dc.contributor.authorOliver, Graham
dc.contributor.authorRuskuc, Nik
dc.contributor.authorThomas, Richard M.
dc.identifier.citationCain , 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 .
dc.identifier.otherPURE: 2338306
dc.identifier.otherPURE UUID: 011e98ad-56c8-48d1-8b0e-ab3a4e91d28f
dc.identifier.otherWOS: 000278029300011
dc.identifier.otherScopus: 77952952975
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702061
dc.description.abstractAn 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.relation.ispartofTheory of Computing Systemsen
dc.rightsThis is an author version of this article. The original publication, (c) Springer Science+Business Media, LLC 2009, is available at www.springerlink.comen
dc.subjectAutomatic presentationen
dc.subjectSemigroup constructionen
dc.subjectClifford semigroupen
dc.subjectCompletely simple semigroupen
dc.subjectQA Mathematicsen
dc.titleAutomatic presentations and semigroup constructionsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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