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. Moreover, we show properties of finite and compact elements of such lattice effect algebras.

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