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SIGMA 6 (2010), 001, 8 pages arXiv:1001.0950
https://doi.org/10.3842/SIGMA.2010.001
Contribution to the Proceedings of the 5-th Microconference Analytic and Algebraic Methods V
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
Zdenka Riecanová
Department of Mathematics,
Faculty of Electrical Engineering and Information Technology,
Slovak University of Technology, Ilkovicova 3,
SK-812 19 Bratislava, Slovak Republic
Received September 29, 2009, in final form January 04, 2010; Published online January 06, 2010
Abstract
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.
Key words:
effect algebra; state; sharp element; center; compatibility center.
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