Kybernetika 42 no. 2, 143-150, 2006

Archimedean atomic lattice effect algebras in which all sharp elements are central

Zdenka Riečanová


We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.