On tolerance lattices of algebras in congruence modular varieties
type: Item
instance of: scholarly article
title: On tolerance lattices of algebras in congruence modular varieties
zbMATH Open document ID: 1049.08007
DOI: 10.1023/A:1024643815068
author: Gábor Czédli
author: Eszter K. Horváth
author: Sándor Radeleczki
published in: Acta Mathematica Hungarica
publication date: 2004-09-07T00:00:00Z
review text: We recall that a lattice \(L\) with \(0\) is called \(0\)-modular if there is no \(N_5\) sublattice of \(L\) including \(0\); a bounded lattice \(L\) is called \(0-1\) modular if no \(N_5\) sublattice of \(L\) includes both \(0\) and \(1\). The purpose of this paper is to extend known results on tolerance lattices of lattices to tolerance lattices of more generalized algebras. The authors prove that the tolerance lattice \(\operatorname{Tol} A\) of an algebra \(A\) from a congruence modular variety \(V\) is \(0-1\) modular and satisfies the general disjointness property (that is, if \(\alpha, \beta, \gamma \in \operatorname{Tol} A\), \(\alpha\wedge\beta = (\alpha \vee \beta)\wedge \gamma = 0\) imply \(\alpha\wedge (\beta\vee \gamma) = 0\)). If \(V\) is congruence distributive, then the lattice \(\operatorname{Tol} A\) is pseudocomplemented; if \(V\) admits a majority term, then \(\operatorname{Tol} A\) is \(0\)-modular.
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 2099063
zbMATH Keywords: tolerance relation
zbMATH Keywords: congruence modularity
zbMATH Keywords: congruence distributivity
zbMATH Keywords: pseudocomplement
zbMATH Keywords: 0-modular lattice
zbMATH Keywords: joint disjointness property
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: a:1024643815068
OpenAlex ID: W1610940513
description: scientific article; zbMATH DE number 2099063