Archimedean atomic lattice effect algebras in which all sharp elements are central
Zdenka Riečanová · Czech digital mathematics library · 2006
summary: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.