Lattices characterized by their sublattice-lattices
type: Item
instance of: scholarly article
title: Lattices characterized by their sublattice-lattices
zbMATH Open document ID: 0903.06001
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: For a lattice \(L\) let Sub\((L)\) denote the lattice of all sublattices of \(L\) and \(L^d\) the dual of \(L\). It is proved that if \(L\) and \(K\) are lattices with Sub\((L)\cong \text{Sub} (K)\) and \(L\) is weakly complemented or \(L\) is modular and ordinal sum indecomposable or \(L\) is semimodular, strongly atomic and ordinal sum indecomposable, then \(L\cong K\) or \(L \cong K^d\). Hence, a complemented modular lattice \(L\) is characterized by Sub\((L)\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06Cxx
zbMATH DE Number: 1226213
zbMATH Keywords: lattice of sublattices
zbMATH Keywords: semimodular lattice
zbMATH Keywords: weakly complemented lattice
zbMATH Keywords: modular lattice
author: Géza Takách
MaRDI profile type: Publication
full work available at URL: s000120050026
OpenAlex ID: W137518412
DOI: 10.1007/S000120050026
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description: scientific article; zbMATH DE number 1226213