Congruence modularity implies the Arguesian law for single algebras with a difference term
type: Item
instance of: scholarly article
title: Congruence modularity implies the Arguesian law for single algebras with a difference term
zbMATH Open document ID: 0930.08004
author: Paolo Lipparini
published in: Journal of Algebra
publication date: 2000-02-06T00:00:00Z
review text: A general commutator theory which was developed for algebras belonging to a congruence modular variety is used to improve known results or give simpler proofs to such results and to (partially) solve some problems. Commutator theory is extended to a somewhat larger setting. Generalizing a result of Freese and Jónsson, it is proved that the congruence lattice of a congruence modular algebra having a difference term is Arguesian. A difference term on an algebra \({\mathbb A}=(A,F)\) is a ternary term \(d\) on \({\mathbb A}\) satisfying \(d(x,y,y)=x\) for all \(x,y\in A\) and \(d(x,x,y) [\alpha,\alpha] y\) for all \(\alpha\in\text{Con }{\mathbb A}\) and all \((x,y)\in\alpha\). Here \([\alpha,\beta]\) denotes the commutator of \(\alpha,\beta\in\text{Con }{\mathbb A}\).
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 08B10
zbMATH DE Number: 1346324
zbMATH Keywords: commutator
zbMATH Keywords: congruence modular variety
zbMATH Keywords: difference term
zbMATH Keywords: Arguesian law
zbMATH Keywords: congruence lattice
zbMATH Keywords: congruence modular algebra
MaRDI profile type: Publication
full work available at URL: jabr.1999.7874
OpenAlex ID: W1981745611
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DOI: 10.1006/JABR.1999.7874
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description: scientific article; zbMATH DE number 1346324