Publication details
Homogeneous orthocomplete effect algebras are covered by MV-algebras
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | FUZZY SETS AND SYSTEMS |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.fss.2012.07.009 |
| Field | General mathematics |
| Keywords | Homogeneous effect algebra; Orthocomplete effect algebra; Lattice effect algebra; Center; Atom; Sharp element; Meager element; Hypermeager element; Ultrameager element |
| Description | The aim of our paper is twofold. First, we thoroughly study the sets of meager and hypermeager elements. Second, we study a common generalization of orthocomplete and lattice effect algebras. We show that every block of an Archimedean homogeneous effect algebra satisfying this generalization is lattice ordered. Hence such effect algebras can be covered by ranges of observables. As a corollary, this yields that every block of a homogeneous orthocomplete effect algebra is lattice ordered. Therefore finite homogeneous effect algebras are covered by MV-algebras. (C) 2012 Elsevier B.V. All rights reserved. |