Modularity, Atomicity and States in Archimedean Lattice Effect Algebras - Paseka, J. (Symmetry, Integrability and Geometry: Methods and Applications, 2010)
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.