Homogeneous orthocomplete effect algebras are covered by MV-algebras

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.