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Title: Automatic presentations and semigroup constructions
Authors: Cain, Alan J.
Oliver, Graham
Ruskuc, Nik
Thomas, Richard M.
Keywords: Automatic presentation
Semigroup construction
Clifford semigroup
Completely simple semigroup
QA Mathematics
Issue Date: Aug-2010
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 . , 10.1007/s00224-009-9216-4
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.
Version: Postprint
Status: Peer reviewed
ISSN: 1432-4350
Type: Journal article
Rights: This is an author version of this article. The original publication, (c) Springer Science+Business Media, LLC 2009, is available at
Appears in Collections:Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
University of St Andrews Research
Applied Mathematics Research
Pure Mathematics Research

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