Publication details

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



Year of publication 2012
Type Article in Periodical
Magazine / Source Soft computing
MU Faculty or unit

Faculty of Science

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.
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