Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

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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Дата:2010
Автор: Paseka, J.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2010
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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spelling irk-123456789-1460932019-02-08T01:23:53Z Modularity, Atomicity and States in Archimedean Lattice Effect Algebras Paseka, J. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146093 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 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.
format Article
author Paseka, J.
spellingShingle Paseka, J.
Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Paseka, J.
author_sort Paseka, J.
title Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
title_short 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_sort modularity, atomicity and states in archimedean lattice effect algebras
publisher Інститут математики НАН України
publishDate 2010
url http://dspace.nbuv.gov.ua/handle/123456789/146093
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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT pasekaj modularityatomicityandstatesinarchimedeanlatticeeffectalgebras
first_indexed 2023-05-20T17:23:48Z
last_indexed 2023-05-20T17:23:48Z
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