More about sharp and meager elements in Archimedean atomic lattice effect algebras

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Authors	PASEKA Jan NIEDERLE Josef
Year of publication	2012
Type	Article in Periodical
Magazine / Source	Soft computing
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.springerlink.com/content/1271803j0uj5646x/
Doi	http://dx.doi.org/10.1007/s00500-011-0738-8
Field	General mathematics
Keywords	Lattice effect algebra; Center; Atom; MacNeille completion; Sharp element; Meager element
Description	The aim of our paper is twofold. First, we thoroughly study the set of meager elements M(E), the center C(E) and the compatibility center B(E) in the setting of atomic Archimedean lattice effect algebras E. The main result is that in this case the center C(E) is bifull (atomic) iff the compatibility center B(E) is bifull (atomic) whenever E is sharply dominating. As a by-product, we give a new description of the smallest sharp element over x is an element of E via the basic decomposition of x: Second, we prove the Triple Representation Theorem for sharply dominating atomic Archimedean lattice effect algebras.
Related projects:	Mathematical structures and their physical applications