Every finitely generated submonoid of a free monoid has a finite Malcev's presentation
type: Item
instance of: scholarly article
title: Every finitely generated submonoid of a free monoid has a finite Malcev's presentation
zbMATH Open document ID: 0677.20046
DOI: 10.1016/0022-4049(89)90043-1
author: Jean-Claude Spehner
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: Given a binary relation \(\rho\) on the free monoid \(\Sigma^*\), denote by \(m(\rho)\) the smallest congruence on \(\Sigma^*\) containing \(\rho\) such that the quotient \(\Sigma^*/m(\rho)\) can be embedded in a group. A monoid \(M\) is said to be Mal'cev presented by \((\Sigma,\rho)\) if \(M\simeq \Sigma^*/m(\rho)\). While there are finitely generated submonoids of a free monoid which are not finitely presented or even do not admit a finite cancellative presentation [the author, Semigroup Forum 14, 295-329 (1977; Zbl 0477.20037)], the paper shows that such a submonoid always admits a finite Mal'cev presentation. The proof of this result gives an effective construction of such a presentation.
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 4109029
zbMATH Keywords: free monoids
zbMATH Keywords: congruences
zbMATH Keywords: finitely generated submonoids
zbMATH Keywords: finite Mal'cev presentations
reviewed by: Jorge Almeida
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90043-1
OpenAlex ID: W2001084673
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description: scientific article; zbMATH DE number 4109029