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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 003, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.003 (Mi sigma460) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

Jan Paseka

Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic
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DOI: https://doi.org/10.3842/SIGMA.2010.003
Abstract: Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there exists an $(o)$-continuous state $\omega$ on $E$, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.
Keywords: effect algebra; state; modular lattice; finite element; compact element.
Received: September 29, 2009; in final form January 7, 2010; Published online January 8, 2010
Bibliographic databases:
Document Type: Article
MSC: 06C15; 03G12; 81P10
Language: English
Citation: Jan Paseka, “Modularity, Atomicity and States in Archimedean Lattice Effect Algebras”, SIGMA, 6 (2010), 003, 9 pp.
Citation in format AMSBIB
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\paper Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
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    		Symmetry, Integrability and Geometry: Methods and Applications
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