Continuous lattice effect algebras admitting order-continuous states
type: Item
instance of: scholarly article
title: Continuous lattice effect algebras admitting order-continuous states
zbMATH Open document ID: 1022.03047
DOI: 10.1016/S0165-0114(02)00141-0
author: Z. Riečanová
published in: Fuzzy Sets and Systems
publication date: 2003-05-27T00:00:00Z
review text: Lattice effect algebras give a common generalization of orthomodular lattices and MV-algebras. This paper gives a necessary and sufficient condition for the existence of a faithful order-continuous state on a complete modular atomic effect algebra. By generalizing \textit{I. Kaplansky}'s famous theorem [Ann. Math. (2) 61, 524-541 (1955; Zbl 0065.01801)] that every complete modular ortholattice is order-continuous, the author shows that every complete modular atomic effect algebra is order-continuous.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 1917787
zbMATH Keywords: MV-algebra
zbMATH Keywords: order continuity
zbMATH Keywords: effect algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1917787