Lattice uniformities and modular functions on orthomodular lattices
type: Item
instance of: scholarly article
title: Lattice uniformities and modular functions on orthomodular lattices
zbMATH Open document ID: 0834.06013
DOI: 10.1007/BF01111744
author: Hans Weber
published in: Order
publication date: 1996-02-01T00:00:00Z
review text: Traynor's decomposition for group-valued set functions is generalized to exhaustive modular functions. It is shown that the lattice of exhaustive (lattice-) uniformities on an orthomodular lattice \(L\) is a complete Boolean algebra isomorphic to the centre of a quotient completion of \(L\).
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06F30
zbMATH DE Number: 828182
zbMATH Keywords: lattice of exhaustive uniformities
zbMATH Keywords: decomposition
zbMATH Keywords: exhaustive modular functions
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: complete Boolean algebra
zbMATH Keywords: centre
zbMATH Keywords: quotient completion
reviewed by: Gudrun Kalmbach
MaRDI profile type: Publication
cites work: Q5662632
cites work: Decompositions of set functions
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cites work: Orthomodular structures as quantum logics. Transl. from the Slovak
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cites work: The Lebesgue Decomposition for Group-Valued Set Functions
cites work: Unabhaengige Topologien, Zerlegung von Ringtopologien
cites work: Topological Boolean rings. Decomposition of finitely additive set functions
cites work: Uniform lattices. I: A generalization of topological Riesz spaces and topological Boolean rings
full work available at URL: https://doi.org/10.1007/bf01111744
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description: scientific article; zbMATH DE number 828182