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    Modularity, Atomicity and States in Archimedean Lattice Effect Algebras

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    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 EE that is not an orthomodular lattice there exists an (o)(o)-continuous state ω\omega on EE, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras
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