Finite homogeneous and lattice ordered effect algebras Original Research Article

We prove that for every finite homogeneous effect algebra E there exists a finite orthoalgebra O(E) and a surjective full morphism φE : O(E)→E. If E is lattice ordered, then O(E) is an orthomodular lattice. Moreover, φE preserves blocks in both directions: the (pre)image of a block is always a block.