Finite homotopy bases of one-relator monoids
type: Item
instance of: scholarly article
title: Finite homotopy bases of one-relator monoids
zbMATH Open document ID: 0961.20045
published in: Journal of Algebra
publication date: 2001-03-06T00:00:00Z
review text: The author continues his studies of homotopy bases of monoids [J. Pure Appl. Algebra 130, No. 2, 159-195 (1998; Zbl 0932.20053)]. A monoid \(M\) which has a presentation of type \((\Sigma,e)\), \(e\in\Sigma^*\times\Sigma^*\), is said to be a one-relator monoid. A parallel relation \(\parallel\) on the derivation graph of \(M\) is defined in a natural way consisting of all pairs \((p,q)\) with the same source and the same target. Any equivalence relation contained in \(\parallel\) and satisfying certain conditions is called a homotopy relation and any generating subset of \(\parallel\) is called a homotopy base. The main theorem states that every one-relator monoid has a finite homotopy base.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 68Q42
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55P99
zbMATH DE Number: 1502164
zbMATH Keywords: one-relator monoids
zbMATH Keywords: rewriting systems
zbMATH Keywords: finite homotopy bases
zbMATH Keywords: presentations
zbMATH Keywords: derivation graphs
zbMATH Keywords: equivalences
author: Yuji Kobayashi
reviewed by: Peeter Normak
MaRDI profile type: Publication
full work available at URL: jabr.1999.8251
OpenAlex ID: W2002862353
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DOI: 10.1006/JABR.1999.8251
description: scientific article; zbMATH DE number 1502164