Sharply Dominating MV-Effect Algebras

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Authors	PASEKA Jan RIEČANOVÁ Zdenka KALINA Martin OLEJČEK Vladimír
Year of publication	2011
Type	Article in Periodical
Magazine / Source	International Journal of Theoretical Physics
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.springerlink.com/content/92867r1358519332/
Doi	http://dx.doi.org/10.1007/s10773-010-0338-x
Field	General mathematics
Keywords	Lattice effect algebra; MV-effect algebra; Sharp element; Sharply dominating effect algebra; Atom; Atomic
Description	Some open questions on Archimedean atomic MV-effect algebras are answered. Namely we prove that there are Archimedean atomic MV-effect algebras which are not sharply dominating. Equivalently, they don't have a basic decomposition of elements. Moreover, if their set of sharp elements (their center) is a complete lattice then they need not be complete lattices. The existence of infinite orthogonal sums of their elements is discussed.
Related projects:	Mathematical structures and their physical applications