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Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Інший ID:
2010 Mathematics Subject Classification: 06C15; 03G12; 81P10
Посилання:
Modularity, Atomicity and States in Archimedean Lattice Effect Algebras / J. Paseka // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 36 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the 5-th Microconference “Analytic and Algebraic Methods V”. The full collection is available at http://www.emis.de/journals/SIGMA/Prague2009.html
We gratefully acknowledge financial support of the Ministry of Education of the Czech Republic under the project MSM0021622409. We also thank the anonymous referees for the very thorough reading and contributions to improve our presentation of the paper.
Дата:
2010
Переглядів:
566
Завантажень:
251
Анотація:
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 ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.
