Almost distributive sublattices and congruence heredity
type: Item
instance of: scholarly article
title: Almost distributive sublattices and congruence heredity
zbMATH Open document ID: 1122.08001
author: John W. Snow
published in: Algebra Universalis
publication date: 2007-09-03T00:00:00Z
review text: Let \(L\) be the congruence lattice of a finite algebra \(A\). If every 0-1 sublattice of \(L\) is also the congruence lattice of an algebra with the same universe as \(A\), then \(L\) is called a hereditary congruence lattice. If every 0-1 sublattice of \(L^n\) is the congruence lattice of an algebra on \(A^n\) for every \(n\geq 1\), then \(L\) is named a power-hereditary congruence lattice. It is known that every congruence lattice representation of \(N_5\) is power-hereditary. Now the author gives an extension of the former results by proving that any congruence lattice representation of a finite lattice obtained by doubling a convex subset of a distributive lattice is hereditary. A number of open problems are posed.
reviewed by: Jaromír Duda
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 5186247
zbMATH Keywords: primitive positive formula
zbMATH Keywords: hereditary congruence lattice
zbMATH Keywords: congruence lattice
MaRDI profile type: Publication
full work available at URL: s00012-007-2010-8
OpenAlex ID: W2041997995
DOI: 10.1007/S00012-007-2010-8
description: scientific article; zbMATH DE number 5186247