Regular congruence-preserving extensions of lattices.
type: Item
instance of: scholarly article
title: Regular congruence-preserving extensions of lattices.
zbMATH Open document ID: 1058.06008
DOI: 10.1007/PL00000332
author: E. T. Schmidt
author: G. Grätzer
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: The authors prove that every lattice \(L\) has a congruence-preserving extension to a regular lattice \(\bar L\) where every compact congruence of \(\bar L\) is principal. The construction of \(\bar L\) is done by iterating a construction of the first author and F. Wehrung and taking direct products. They also discuss the case of a finite lattice \(L\) for which \(\bar L\) can be chosen to be finite, and of a lattice \(L\) with zero, in which case \(\bar L\) can be chosen to have zero and the extension can be chosen to preserve zero.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 2158736
zbMATH Keywords: regular lattice
zbMATH Keywords: principal congruence
zbMATH Keywords: compact congruence
MaRDI profile type: Publication
full work available at URL: pl00000332
OpenAlex ID: W1987233195
description: scientific article; zbMATH DE number 2158736