Lattice ordered effect algebras

Abstract.

The purpose of this paper is to discuss some structural properties of lattice ordered effect algebras. We will use these structural properties to find certain lattices and classes of lattices that do not admit an effect algebra structure. Finally, using these structural properties, we will show that if L is the face lattice of a convex polytope in $ R^3 $ with more than 3 vertices, then L does not admit an effect algebra structure.