Lattices with finite \(W\)-covers
type: Item
instance of: scholarly article
title: Lattices with finite \(W\)-covers
zbMATH Open document ID: 0901.06004
DOI: 10.1007/BF01236758
published in: Algebra Universalis
publication date: 1998-11-24T00:00:00Z
review text: A lattice \(\widetilde L\) is called a finite \(W\)-cover of a finite lattice \(L\) if \(\widetilde L\) satisfies Whitman's condition \(W\) and there is a homomorphism \(f\) of \(\widetilde L\) onto \(L\) such that whenever \(g\) is a homomorphism of a lattice \(R\) satisfying \(W\) onto \(L\) then \(g=f\cdot h,\) where \(h\) is a homomorphism of \(R\) onto \(\widetilde L\). The purpose of the paper is to show that the existence of a finite \(W\)-cover for a given lattice is decidable. It is shown that for a given finite lattice \(L\) and a subset \(A\) of \(L,\) the existence of a finite lattice \(Q\) and homomorphism \(f\) of \(Q\) onto \(L\) such that whenever \(I=[a\wedge b,c\vee d]\) is an interval in \(Q\) then either \(I\cap \{a,b,c,d\}\not =\emptyset \) or \(f(I)\cap A\not=\emptyset \) is decidable. It is proved that for a finite \(W\)-cover \(\widetilde L\) of \(L\), \(|\widetilde L|\leq 86\cdot| L|\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B25
zbMATH DE Number: 1226545
zbMATH Keywords: finite lattice
zbMATH Keywords: \(W\)-cover
zbMATH Keywords: Whitman's condition
zbMATH Keywords: \(W\)-failure
zbMATH Keywords: decidability
author: Václav Slaví k
MaRDI profile type: Publication
cites work: A Simple Solution to the Word Problem for Lattices
cites work: Distributive lattices with finite projective covers
cites work: Doubling Constructions in Lattice Theory
cites work: An application of Whitman's condition to lattices with no infinite chains
full work available at URL: https://doi.org/10.1007/bf01236758
OpenAlex ID: W2322544074
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description: scientific article; zbMATH DE number 1226545