The matrix of a slim semimodular lattice
type: Item
instance of: scholarly article
title: The matrix of a slim semimodular lattice
zbMATH Open document ID: 1257.06004
author: Gábor Czédli
published in: Order
publication date: 2012-03-23T00:00:00Z
review text: Slim semimodular lattices are particular planar lattices: they do not admit any 3-element antichain of join irreducibles. The first main result of the paper under review establishes a 1-1-correspondence between such lattices, which are not decomposable as the gluing of two intervals, and certain join congruences on the direct product of two chains. The latter, again, are shown to be in 1-1-correspondence with certain subsets of intervals, isomorphic to \(\mathbf{2}\times \mathbf{2}\), of these direct products -- also to be described in terms of \(0\)-\(1\)-matrices. Background of these investigations is a detailed study of the lattice theory behind the Jordan-Hölder theorem, given by the author and \textit{E. T. Schmidt} in [Algebra Univers. 66, No. 1--2, 69--79 (2011; Zbl 1233.06006)].
reviewed by: Christian Herrmann
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 6018078
zbMATH Keywords: semimodular lattice
zbMATH Keywords: planar lattice
zbMATH Keywords: slim lattice
MaRDI profile type: Publication
full work available at URL: s11083-011-9199-z
OpenAlex ID: W2063698191
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DOI: 10.1007/S11083-011-9199-Z
description: scientific article; zbMATH DE number 6018078