Slim semimodular lattices. I. A visual approach
type: Item
instance of: scholarly article
title: Slim semimodular lattices. I. A visual approach
zbMATH Open document ID: 1257.06005
author: Gábor Czédli
author: E. T. Schmidt
published in: Order
publication date: 2012-11-07T00:00:00Z
review text: Planar lattices have a diagram to be depicted in the plane. This nice paper under review proves this approach to be very appropriate for finite semimodular lattices which are slim, i.e., do not admit any 3-element antichain of join irreducibles. The first main result shows that any such lattice can be obtained from chains by iterative extensions of a very simple kind (adding `corners' and `forks', respectively); the second one shows that any such lattice can be obtained from the product of two chains by first adding forks and then deleting corners.
reviewed by: Christian Herrmann
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 6102618
zbMATH Keywords: semimodular lattice
zbMATH Keywords: slim lattice
zbMATH Keywords: planar lattice
zbMATH Keywords: join-homomorphism
zbMATH Keywords: contour
zbMATH Keywords: fork
zbMATH Keywords: corner
MaRDI profile type: Publication
full work available at URL: s11083-011-9215-3
OpenAlex ID: W2037712376
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DOI: 10.1007/S11083-011-9215-3
description: scientific article; zbMATH DE number 6102618