Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type.
type: Item
instance of: scholarly article
title: Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type.
zbMATH Open document ID: 1338.06007
DOI: 10.1134/S0037446615040072
author: A. G. Gein
author: Mikhaĭl P. Shushpanov
published in: Siberian Mathematical Journal
publication date: 2015-10-29T00:00:00Z
review text: It is long known (Grätzer-Schmidt) that in every lattice the sublattice generated by three elements, two of which are standard, is distributive. In the same spirit the paper under review exhibits conditions on three elements of any lattice that guarantee the modularity of the generated sublattice \(S\). Specifically, all combinations of left-modularity, right-modularity, and dual right-modularity that suffice for the modularity of \(S\) are classified. The free modular lattice on three generators is invoked for this purpose.
reviewed by: Marcel Wild
Mathematics Subject Classification ID: 06C05
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B25
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 6501742
zbMATH Keywords: modular lattices
zbMATH Keywords: modular elements
zbMATH Keywords: modularity
zbMATH Keywords: sublattices generated by three elements
zbMATH Keywords: free modular lattices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6501742