Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

Details Modularity, Atomicity and States in Archimedean Lattice Effect Algebras Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

2010-01-08

arxiv.org/abs/1001.1322v1

SIGMA 6 (2010), 003, 9 pages

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2010.003

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 $\omega$ on $E$, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.

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