Block-finite atomic orthomodular lattices
type: Item
instance of: scholarly article
title: Block-finite atomic orthomodular lattices
zbMATH Open document ID: 0786.06007
DOI: 10.1016/0022-4049(93)90058-2
author: M. C. Fu
published in: Journal of Pure and Applied Algebra
publication date: 1994-05-06T00:00:00Z
review text: A block-finite orthomodular lattice \(L\) has only finitely many blocks, i.e. maximal Boolean subalgebras. It is shown that the MacNeille completion of \(L\) is an orthomodular lattice. Assume \(L\) is complete. Then \(L\) is atomic iff the interval topology on \(L\) is Hausdorff. Let \(M\) be a complete, (0)-continuous, commutator-finite orthomodular lattice with trivial center. Then \(M\) is atomic. For a complete, (0)-continuous, atomless orthomodular lattice \(M\), the conditions: \(M\) is a Boolean algebra, \(M\) is block-finite, and \(M\) is commutator-finite, are equivalent. For compact topological orthomodular lattices \(L\) some characterizations are given for \(L\) to be profinite, i.e. isomorphic with a direct product of finite orthomodular lattices.
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06B30
zbMATH DE Number: 445052
zbMATH Keywords: block-finite orthomodular lattice
zbMATH Keywords: MacNeille completion
zbMATH Keywords: commutator- finite orthomodular lattice
zbMATH Keywords: Boolean algebra
zbMATH Keywords: compact topological orthomodular lattices
zbMATH Keywords: profinite
reviewed by: Gudrun Kalmbach
MaRDI profile type: Publication
full work available at URL: 0022-4049(93)90058-2
OpenAlex ID: W2047978536
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description: scientific article; zbMATH DE number 445052