Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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