Presentations of general products of monoids
type: Item
instance of: scholarly article
title: Presentations of general products of monoids
zbMATH Open document ID: 0914.20051
author: T. G. Lavers
published in: Journal of Algebra
publication date: 1999-06-20T00:00:00Z
review text: Let \(S\) and \(T\) be two semigroups, \(\lambda\colon T\times S\to T\) be a right action of \(S\) on \(T\) and \(\rho\colon T\times S\to S\) be a left action of \(T\) on \(S\). If \(\lambda\) and \(\rho\) satisfy some conditions the set \(S\times T\) endowed with the binary operation \((a,x)\circ(b,y)=(a\rho(x,b),\lambda(x,b)y)\) is a semigroup, called a general product of \(S\) and \(T\), and denoted \(S\times T\). If \(S\) and \(T\) are monoids and \(\lambda,\rho\) satisfy some supplementary conditions then \(S\times T\) is also a monoid. The main results of the paper give conditions under which a general product of two finitely presented semigroups is finitely presented. Two examples that illustrate the theoretical results are included. Presentations are obtained for: (1) the Bruck-Reilly extension of a finitely presented monoid; (2) the symmetric groups.
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1218682
zbMATH Keywords: general products
zbMATH Keywords: finitely presented semigroups
zbMATH Keywords: Bruck-Reilly extensions
zbMATH Keywords: finitely presented monoids
reviewed by: Marin Guţan
MaRDI profile type: Publication
full work available at URL: jabr.1997.7389
OpenAlex ID: W2043655726
cites work: Constructions and presentations for monoids
cites work: Q4087417
cites work: Zappa products
cites work: Bilateral semidirect products of transformation semigroups
cites work: A Remark on Primary Ideals
DOI: 10.1006/JABR.1997.7389
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description: scientific article; zbMATH DE number 1218682