Residual finiteness of a class of semigroups presented by a single relation
type: Item
instance of: scholarly article
title: Residual finiteness of a class of semigroups presented by a single relation
zbMATH Open document ID: 0807.20047
DOI: 10.1007/BF02573667
author: Gerard Lallement
author: Laurent Rosaz
published in: Semigroup Forum
publication date: 1995-02-28T00:00:00Z
full work available at URL: https://eudml.org/doc/135309
review text: A semigroup \(S\) is said to be residually finite if for every pair of elements \(x\), \(y\) in \(S\), \(x \neq y\), there exists a congruence \(\rho\) on \(S\) such that \(S/\rho\) is finite and \([x]_ \rho \neq [y]_ \rho\). In the paper it is proved that the semigroups \(S_ k\) presented by \(\langle a,b;\;b(ab)^ kb = ab\rangle\) (\(k \geq 0\)) are all residually finite. Connections between the residual finiteness of a semigroup \(S\) and decidability of the word problem for presentations of \(S\) are discussed.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M15
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 549061
zbMATH Keywords: residually finite semigroups
zbMATH Keywords: congruences
zbMATH Keywords: residual finiteness
zbMATH Keywords: decidability
zbMATH Keywords: word problem for presentations
reviewed by: Vladimir Fleischer
MaRDI profile type: Publication
cites work: Q4079524
cites work: Some Connections between Residual Finiteness, Finite Embeddability and the Word Problem
cites work: Q3853827
cites work: Sur les monoides à un relateur qui sont des groupes
OpenAlex ID: W2002315582
description: scientific article; zbMATH DE number 549061