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Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
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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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Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
Інший ID:
2010 Mathematics Subject Classification: 06C15; 03G12; 81P10
Посилання:
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements / Z. Riecanová // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 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.
This work was supported by the Slovak Research and Development Agency under the contract No. APVV–0375–06 and the grant VEGA-2/0032/09 of MS SR. The author wishes to express his thanks to referees for many stimulating questions and suggestions during the preparation of the paper, which helped to improve it.
Дата:
2010
Переглядів:
631
Завантажень:
273
Анотація:
We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra E is separable and modular then there exists a faithful state on E. Further, if an atomic lattice effect algebra is densely embeddable into a complete lattice effect algebra ^E and the compatiblity center of E is not a Boolean algebra then there exists an (o)-continuous subadditive state on E.
