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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2010
1. Verfasser: Paseka, J.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2010
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146093
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Zitieren: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
id nasplib_isofts_kiev_ua-123456789-146093
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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
spellingShingle Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Paseka, J.
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
author Paseka, J.
author_facet Paseka, J.
publishDate 2010
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
work_keys_str_mv AT pasekaj modularityatomicityandstatesinarchimedeanlatticeeffectalgebras
first_indexed 2025-12-07T18:08:39Z
last_indexed 2025-12-07T18:08:39Z
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