A note on atomistic weak congruence lattices
type: Item
instance of: scholarly article
title: A note on atomistic weak congruence lattices
zbMATH Open document ID: 1221.06003
author: Branimir Šešelja
author: Andreja Tepavčević
published in: Discrete Mathematics
publication date: 2008-11-12T00:00:00Z
review text: An element \(s\) of a lattice \(L\) is called distributive if \(s\vee(x \wedge y)=(s\vee x)\wedge(s\vee y)\), \(x,y\in L\). The dual identity defines codistributive elements. First, it is proved that a codistributive element \(s\) in an atomistic algebraic lattice \(L\) has a complement \(s'\) which is distributive; the kernels of the homomorphisms \(x\mapsto x \wedge s\), \(x\in L\), and \(x\mapsto x\vee s'\), \(x\in L\), coincide. Then some consequences to weak congruence lattices of algebras are derived. Namely, algebras with atomistic weak congruence lattices are studied in detail.
reviewed by: Jaromír Duda
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 5365270
zbMATH Keywords: codistributive element
zbMATH Keywords: atomistic lattice
zbMATH Keywords: weak congruences
zbMATH Keywords: CEP
zbMATH Keywords: CIP
MaRDI profile type: Publication
full work available at URL: j.disc.2007.04.046
OpenAlex ID: W2075597241
cites work: Q4165427
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cites work: Weak congruences in universal algebra
cites work: Q4839144
DOI: 10.1016/J.DISC.2007.04.046
description: scientific article; zbMATH DE number 5365270