Sharply Dominating MV-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	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