Automatic completely-simple semigroups
type: Item
instance of: scholarly article
title: Automatic completely-simple semigroups
zbMATH Open document ID: 0997.20050
DOI: 10.1023/A:1015632704977
author: N. Ruškuc
author: C. M. Campbell
author: E. F. Robertson
author: Richard M. Thomas
published in: Acta Mathematica Hungarica
publication date: 2002-11-03T00:00:00Z
review text: The main result of the article states that a Rees matrix semigroup \(M[H;I,J;P]\) with finite \(I\) and \(J\) is automatic if and only if the group \(H\) is automatic. As a corollary, it is verified that an automatic Rees matrix semigroup is finitely presented. The authors also show that automatic completely simple semigroups are characterized by the fellow traveller property. One more result is that the existence of an automatic structure for a Rees matrix semigroup is independent of the choice of the generating set.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20M35
Mathematics Subject Classification ID: 68Q45
zbMATH DE Number: 1822374
zbMATH Keywords: automatic groups
zbMATH Keywords: automatic semigroups
zbMATH Keywords: regular languages
zbMATH Keywords: completely simple semigroups
zbMATH Keywords: Rees matrix semigroups
zbMATH Keywords: finitely presented semigroups
reviewed by: Boris Vernikov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1822374