Representing a monotone map by principal lattice congruences
type: Item
instance of: scholarly article
title: Representing a monotone map by principal lattice congruences
zbMATH Open document ID: 1374.06007
author: Gábor Czédli
published in: Acta Mathematica Hungarica
publication date: 2017-03-31T00:00:00Z
full work available at URL: actamathhung 047 001 content.pdf
review text: For a lattice \(L\), let Princ(\(L\)) denote the ordered set of principal congruences of \(L\). In this paper, the author proves that for each \(0\)-separating bound-preserving monotone map \(f\) between two bounded ordered sets, there are a lattice \(L\) and a sublattice \(K\) of \(L\) such that \(f\) is the map from Princ(\(K\)) to Princ(\(L\)) that sends a principal congruence to the congruence it generates in the larger lattice.
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 6699215
zbMATH Keywords: principal congruence
zbMATH Keywords: lattice congruence
zbMATH Keywords: ordered set
zbMATH Keywords: order
zbMATH Keywords: poset
zbMATH Keywords: quasi-colored lattice
zbMATH Keywords: preordering
zbMATH Keywords: quasiordering
zbMATH Keywords: monotone map
reviewed by: Yuri Movsisyan
MaRDI profile type: Publication
OpenAlex ID: W1132841840
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DOI: 10.1007/S10474-015-0539-0
description: scientific article; zbMATH DE number 6699215