Maximal Subsets of Pairwise Summable Elements in Generalized Effect Algebras

Warning

This publication doesn't include Institute of Computer Science. It includes Faculty of Science. Official publication website can be found on muni.cz.

Authors	RIEČANOVÁ Zdenka JANDA Jiří
Year of publication	2013
Type	Article in Periodical
Magazine / Source	Acta Polytechnica
MU Faculty or unit	Faculty of Science
Citation
Web	http://ojs.cvut.cz/ojs/index.php/ap/article/view/1865
Doi	http://dx.doi.org/10.14311/AP.2013.53.0457
Field	General mathematics
Keywords	(generalized) effect algebra; MV-effect algebra; summability block; compatibility block; linear operators in Hilbert spaces
Description	We show that in any generalized effect algebra (G;+,0) a maximal pairwise summable subset is a sub-generalized effect algebra of (G;+, 0), called a summability block. If G is lattice ordered, then every summability block in G is a generalized MV-effect algebra. Moreover, if every element of G has an infinite isotropic index, then G is covered by its summability blocks, which are generalized MV-effect algebras in the case that G is lattice ordered. We also present the relations between summability blocks and compatibility blocks of G. Counterexamples, to obtain the required contradictions in some cases, are given.
Related projects:	Mathematical structures and their physical applications