Modularity, Atomicity and States in Archimedean Lattice Effect Algebras
Jan Paseka · 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.