Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
نویسنده
چکیده
We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra E is separable and modular then there exists a faithful state on E. Further, if an atomic lattice effect algebra is densely embeddable into a complete lattice effect algebra Ê and the compatiblity center of E is not a Boolean algebra then there exists an (o)-continuous subadditive state on E.
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