Quasi-equational bases for graphs of semigroups, monoids and groups.
type: Item
instance of: scholarly article
title: Quasi-equational bases for graphs of semigroups, monoids and groups.
zbMATH Open document ID: 1228.20045
author: Michał M. Stronkowski
published in: Semigroup Forum
publication date: 2011-05-11T00:00:00Z
review text: The graph of an algebra \(\mathbf A\) is the relational structure \(G(\mathbf A)\) in which the relations are the graphs of the basic operations of \(\mathbf A\). Denote by \(G(\mathcal K)\) the class of all graphs of algebras from a class \(\mathcal K\). The author proves that if \(\mathcal K\) is a class of semigroups possessing a nontrivial member with a neutral element, then \(G(\mathcal K)\) does not have finite quasi-equational bases. As a corollary of this result, a similar result for a nontrivial class \(\mathcal K\) of monoids or groups is received. For contrast the author marks, that if \(\mathcal K\) is a nontrivial class of semigroups with zero multiplication, then the class \(G(\mathcal K)\) has a quasi-equational basis consisting of two quasi-identities.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5886837
zbMATH Keywords: graphs of semigroups
zbMATH Keywords: finite axiomatizability
zbMATH Keywords: finite quasi-equational bases
zbMATH Keywords: quasivarieties of relational structures
reviewed by: Leonid M. Martynov
MaRDI profile type: Publication
full work available at URL: s00233-010-9268-4
OpenAlex ID: W1967998534
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DOI: 10.1007/S00233-010-9268-4
description: scientific article; zbMATH DE number 5886837