Lattices of suborders
type: Item
instance of: scholarly article
title: Lattices of suborders
zbMATH Open document ID: 0924.06009
DOI: 10.1007/BF02679765
published in: Siberian Mathematical Journal
publication date: 1999-10-28T00:00:00Z
review text: The lattices of suborders of partial orders are studied. In particular, the author gives a description for upper semidistributive lattices of suborders, characterizes such lattices for finite orderings (as those satisfying each of the following three conditions: the Freese-Nation minimality condition, the Jónsson property, the McKenzie property), obtains a sufficient condition for a lattice satisfying the Freese-Nation minimality condition to be isomorphic to a sublattice of suborderings (from the proof of this result, the author obtains a new proof of the embedding theorem of \textit{B. Sivák} [Math. Slovaca 28, No. 2, 203-215 (1978; Zbl 0395.06002)]), and describes lattices of suborders that possess the complete Jónsson property introduced by the author.
Mathematics Subject Classification ID: 06B15
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 1353828
zbMATH Keywords: lattice of suborders
zbMATH Keywords: Freese-Nation minimality condition
zbMATH Keywords: Jónsson property
author: M. V. Schwidefsky
reviewed by: Andrei S. Morozov
MaRDI profile type: Publication
cites work: Representations of ordered semigroups and lattices by binary relations
cites work: Q4177619
cites work: On lower bounded lattices.
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cites work: Q4948583
cites work: A class of lattices of quasivarities
full work available at URL: https://doi.org/10.1007/bf02679765
OpenAlex ID: W1978579918
description: scientific article; zbMATH DE number 1353828