Pseudocomplemented lattice effect algebras and existence of states |
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Authors: | Zdenka Rie?anová |
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Affiliation: | Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovi?ova 3, SK-812 19 Bratislava, Slovak Republic |
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Abstract: | We prove that in every pseudocomplemented atomic lattice effect algebra the subset of all pseudocomplements is a Boolean algebra including the set of sharp elements as a subalgebra. As an application, we show families of effect algebras for which the existence of a pseudocomplementation implies the existence of states. These states can be obtained by smearing of states existing on the Boolean algebra of sharp elements. |
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Keywords: | 03G12 06D35 81P10 |
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