More about sharp and meager elements in Archimedean atomic lattice effect algebras
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Soft computing |
| MU Faculty or unit | |
| 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. |
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