Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
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. More...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146093 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716957073080320 |
|---|---|
| author | Paseka, J. |
| author_facet | Paseka, J. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T18:08:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146093 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:08:39Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Paseka, J. 2019-02-07T12:34:09Z 2019-02-07T12:34:09Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 06C15; 03G12; 81P10 https://nasplib.isofts.kiev.ua/handle/123456789/146093 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Modularity, Atomicity and States in Archimedean Lattice Effect Algebras Article published earlier |
| spellingShingle | Modularity, Atomicity and States in Archimedean Lattice Effect Algebras Paseka, J. |
| title | Modularity, Atomicity and States in Archimedean Lattice Effect Algebras |
| title_full | Modularity, Atomicity and States in Archimedean Lattice Effect Algebras |
| title_fullStr | Modularity, Atomicity and States in Archimedean Lattice Effect Algebras |
| title_full_unstemmed | Modularity, Atomicity and States in Archimedean Lattice Effect Algebras |
| title_short | Modularity, Atomicity and States in Archimedean Lattice Effect Algebras |
| title_sort | modularity, atomicity and states in archimedean lattice effect algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146093 |
| work_keys_str_mv | AT pasekaj modularityatomicityandstatesinarchimedeanlatticeeffectalgebras |