On lattices whose congruences form Stone lattices
type: Item
instance of: scholarly article
title: On lattices whose congruences form Stone lattices
zbMATH Open document ID: 0627.06009
DOI: 10.1007/BF01951001
author: C. Malliah
author: P. S. Bhatta
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: A pseudocomplemented distributive lattice is called a Stone lattice if the pseudocomplement \(a^*\) of each element a has a complement. Several authors have studied lattices whose congruences form a Stone lattice. The present paper contains a general description of this class of lattices, and many of the earlier results follow as special cases of the current results. If \(a/b\to c/d\) denotes the fact that the quotient \(a/b\) is weakly projective into \(c/d\), then \(C(L)\) is a Stone lattice iff the pseudocomplement \(\theta^*\) of each congruence \(\theta\) is separable, and \(L\) satisfies: \(a/b\to c/d\) with \(a>b\) and \(c>d\) implies the existence of \(c', d'\) such that \(c\geq c'>d'\geq d\) and \(c'\equiv d'(\theta^{**}_{a/b})\).
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 06D15
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 4019123
zbMATH Keywords: pseudocomplemented distributive lattice
zbMATH Keywords: Stone lattice
zbMATH Keywords: congruences
reviewed by: Melvin F. Janowitz
MaRDI profile type: Publication
cites work: Q4083730
cites work: Q3875978
cites work: Normal, simple and neutral congruences on lattices
cites work: Q5622232
cites work: Q5562610
cites work: On a paper by Iqbalunnisa
cites work: Complemented congruences on complemented lattices
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description: scientific article; zbMATH DE number 4019123