Minimal but inefficient presentations of the semi-direct products of some monoids.
type: Item
instance of: scholarly article
title: Minimal but inefficient presentations of the semi-direct products of some monoids.
zbMATH Open document ID: 1054.20039
author: Yanyan Li
published in: Semigroup Forum
publication date: 2003-03-18T00:00:00Z
review text: A monoid is said to be efficient if it admits an efficient presentation. If some monoid has a presentation that is minimal but not efficient, then this monoid is called inefficient. The results of this paper help to find examples of inefficient monoids. The paper studies presentations of the semidirect product of one-relator monoids by the infinite cyclic monoid. It gives necessary and sufficient conditions for these presentations to be minimal but not efficient, and shows how this result can be applied in several situations. The author makes extensive use of the \(p\)-Cockcroft property of monoid presentations [see \textit{S. J. Pride}, Int. J. Algebra Comput. 5, No. 6, 631-649 (1995; Zbl 0838.20075)], and the equivalence between this property and efficiency. As for the style, the rigor and detail of some definitions contrasts with the slackness shown in others. This fact, combined with a couple of English mistakes, makes the paper a little hard to read, which does not stain its mathematical value.
reviewed by: Hebert Pérez-Rosés
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 1883960
zbMATH Keywords: monoid presentations
zbMATH Keywords: generators and relations
zbMATH Keywords: spherical monoid pictures
zbMATH Keywords: \(p\)-Cockcroft property
zbMATH Keywords: semidirect products of monoids
zbMATH Keywords: Squier complexes
MaRDI profile type: Publication
full work available at URL: s002330010148
OpenAlex ID: W2079289908
DOI: 10.1007/S002330010148
description: scientific article; zbMATH DE number 1883960