Quasiorders and sublattices of distributive lattices
type: Item
instance of: scholarly article
title: Quasiorders and sublattices of distributive lattices
zbMATH Open document ID: 1006.06006
DOI: 10.1023/A:1015291410777
published in: Order
publication date: 2002-08-21T00:00:00Z
review text: The author studies the lattice \(\text{Sub}_{01}(L)\) of all \((0,1)\)-sublattices of a distributive lattice \(L\), using certain compatible quasiorders on the Priestley space of \(L\). The main theorems describe \(\text{Sub}_{01}(L)\) in terms of special quasiorders on the Priestley space of \(L\) and characterize the covering relation in \(\text{Sub}_{01}(L)\) in terms of critical pairs. Special emphasis is laid on the case where \(L\) is finite, where epic sublattices, Frattini sublattices and covers are considered. The author demonstrates that quasiorders may serve as a concept that is suitable to unify the many different representations of sublattices of \(L\) that are found in the literature.
reviewed by: Bohumil František Šmarda
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 1785650
zbMATH Keywords: representation theory
zbMATH Keywords: \((0,1)\)-sublattices
zbMATH Keywords: distributive lattice
zbMATH Keywords: quasiorders
zbMATH Keywords: Priestley space
zbMATH Keywords: covering relation
zbMATH Keywords: critical pairs
author: Jürg Schmid
MaRDI profile type: Publication
full work available at URL: a:1015291410777
OpenAlex ID: W141387809
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description: scientific article; zbMATH DE number 1785650