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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
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
Citation:
Jan Paseka, “Modularity, Atomicity and States in Archimedean Lattice Effect Algebras”, SIGMA, 6 (2010), 003, 9 pp.
Linking options:
https://www.mathnet.ru/eng/sigma460 https://www.mathnet.ru/eng/sigma/v6/p3
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Abstract page: | 269 | Full-text PDF : | 48 | References: | 54 |
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