Generalising congruence regularity for varieties.
type: Item
instance of: scholarly article
title: Generalising congruence regularity for varieties.
zbMATH Open document ID: 1063.08007
DOI: 10.1007/PL00012452
author: Marcel Jackson
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: The concept of \([s,t]\)-regularity of a variety \(\mathcal V\) is introduced for a couple \([s,t]\) of \(n_1\)-ary and \(n_2\)-ary term \(s\) and \(t\) in the signature of \(\mathcal V\). In fact this concept is not new, and it was already treated by \textit{G.\ D.\ Barbour} and \textit{J.\ G.\ Raftery} [Czech.\ Math.\ J.\ 47, 317--325 (1997; Zbl 0927.08001)] in a more general setting. The Mal'tsev condition presented by the author is also a particular case of Theorem 3 in the quoted paper. The author applies this theorem to show that the variety of \(I\)-semigroups is \(x^{-1}x\)-regular and to characterize inverse semigroups having this property.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M07
zbMATH DE Number: 2158808
zbMATH Keywords: 0-regular
zbMATH Keywords: congruence regular variety
zbMATH Keywords: inverse semigroup
zbMATH Keywords: Mal'tsev condition
MaRDI profile type: Publication
full work available at URL: pl00012452
OpenAlex ID: W2087540685
description: scientific article; zbMATH DE number 2158808