Atomic effect algebras with compression bases
- Department of Mathematics and Informatics, Technical University of Civil Engineering in Bucharest, 124 Lacul Tei blv., RO-020396 and 'Ilie Murgulescu' Institute of Physical Chemistry, Romanian Academy, 202 Splaiul Independentei, 060021 Bucharest (Romania)
- Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, 166 27 Prague (Czech Republic)
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
- OSTI ID:
- 21501255
- Journal Information:
- Journal of Mathematical Physics, Vol. 52, Issue 1; Other Information: DOI: 10.1063/1.3533918; (c) 2011 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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