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Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
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 is separable and modular then there exists a
faithful state on . Further, if an atomic lattice effect algebra is densely
embeddable into a complete lattice effect algebra and the
compatiblity center of is not a Boolean algebra then there exists an
-continuous subadditive state on
A representation theorem for MV-algebras
An {\em MV-pair} is a pair where is a Boolean algebra and is
a subgroup of the automorphism group of satisfying certain conditions. Let
be the equivalence relation on naturally associated with . We
prove that for every MV-pair , the effect algebra is an MV-
effect algebra. Moreover, for every MV-effect algebra there is an MV-pair
such that is isomorphic to
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
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