Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Author: Paseka, J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146093
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...