Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146094 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709607268352000 |
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| author | Riecanová, Z. |
| author_facet | Riecanová, Z. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T17:19:02Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146094 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:19:02Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
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| spelling | Riecanová, Z. 2019-02-07T12:36:36Z 2019-02-07T12:36:36Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 06C15; 03G12; 81P10 https://nasplib.isofts.kiev.ua/handle/123456789/146094 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements Article published earlier |
| spellingShingle | Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements Riecanová, Z. |
| title | Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements |
| title_full | Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements |
| title_fullStr | Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements |
| title_full_unstemmed | Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements |
| title_short | Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements |
| title_sort | archimedean atomic lattice effect algebras with complete lattice of sharp elements |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146094 |
| work_keys_str_mv | AT riecanovaz archimedeanatomiclatticeeffectalgebraswithcompletelatticeofsharpelements |