Lattice effect algebras with (o)-continuous faithful valuations
type: Item
instance of: scholarly article
title: Lattice effect algebras with (o)-continuous faithful valuations
zbMATH Open document ID: 0997.03051
DOI: 10.1016/S0165-0114(01)00102-6
author: Z. Riečanová
published in: Fuzzy Sets and Systems
publication date: 2002-05-21T00:00:00Z
review text: Effect algebras have been introduced by \textit{D. J. Foulis} and \textit{M. K. Bennett} [``Effect algebras and unsharp quantum logics'', Found. Phys. 24, 1331-1352 (1994)] to study quantum effects which may be unsharp. The main result of this paper goes as follows: Theorem 5.4. Let there exist an (o)-continuous faithful valuation on a lattice effect algebra \((E;\oplus,0,1)\). Then (i) \(E\) is modular, separable and (o)-continuous; (ii) \(E\) can be supremum and infimum densely embedded into a complete modular, separable and (o)-continuous effect algebra \(\widehat E\); (iii) there is a unique (o)-continuous faithful valuation \(\widehat\omega\) on \(\widehat E\) which extends \(\omega\).
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 1743109
zbMATH Keywords: order continuity
zbMATH Keywords: MacNeille completion
zbMATH Keywords: lattice effect algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1743109