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...
Збережено в:
| Дата: | 2010 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146094 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1460942019-02-08T01:23:29Z Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements Riecanová, Z. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146094 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Riecanová, Z. |
| spellingShingle |
Riecanová, Z. Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Riecanová, Z. |
| author_sort |
Riecanová, Z. |
| title |
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_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_sort |
archimedean atomic lattice effect algebras with complete lattice of sharp elements |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146094 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT riecanovaz archimedeanatomiclatticeeffectalgebraswithcompletelatticeofsharpelements |
| first_indexed |
2023-05-20T17:23:48Z |
| last_indexed |
2023-05-20T17:23:48Z |
| _version_ |
1796153200228696064 |