Modular almost orthogonal quantum logics
type: Item
instance of: scholarly article
title: Modular almost orthogonal quantum logics
zbMATH Open document ID: 0780.06006
DOI: 10.1007/BF00678552
author: Z. Riečanová
author: Sylvia Pulmannová
published in: International Journal of Theoretical Physics
publication date: 1993-01-16T00:00:00Z
review text: An orthomodular lattice (OML) is said to be almost orthogonal if it is atomic and if for every atom \(a\) in \(L\) the set \(B_ a=\{b\in L\mid b\) is an atom in \(L\) and \(b\not\leq a'\}\) is finite. Relations between almost orthogonality and modularity are studied. An almost orthogonal OML is modular if and only if it can be embedded into a direct product of finite modular quantum logics. The class of almost orthogonal modular OMLs is the largest subclass of the class of atomic modular OMLs in which the conditions commutator-finite and block-finite are equivalent.
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 95361
zbMATH Keywords: modularity
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: almost orthogonality
zbMATH Keywords: modular quantum logics
reviewed by: Vladimír Rogalewicz
MaRDI profile type: Publication
cites work: Q5532570
cites work: Commutator-finite orthomodular lattices
cites work: Q4750696
cites work: Q5623714
cites work: Q3989721
cites work: Q3483290
cites work: Q4007199
cites work: Representations of locally compact orthomodular lattices
full work available at URL: https://doi.org/10.1007/bf00678552
OpenAlex ID: W1965674947
description: scientific article; zbMATH DE number 95361