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Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\widehat{E}$ and the compatiblity center of $E$ is not a Boolean algebra then there exists an $(o)$-continuous subadditive state on $E$.
Keywords: effect algebra; state; sharp element; center; compatibility center. 
@article{SIGMA_2010_6_a0,
     author = {Zdenka Rie\v{c}anov\'a},
     title = {Archimedean {Atomic} {Lattice} {Effect} {Algebras} with {Complete} {Lattice} of {Sharp} {Elements}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2010},
     volume = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a0/}
}
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Zdenka Riečanová. Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a0/

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