Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements

[摘要] 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 ^ E and the compatiblity center of E is not a Boolean algebra then there exists an ( o )-continuous subadditive state on E .

[关键词] ef fect algebra;state;sharp element;center;compatibility center