  The aim of our paper is twofold. First, we thoroughly study the set of meager
elements Mea(E) and the set of hypermeager elements HMea(E) in the setting of
homogeneous effect algebras E. Second, we study the property (W+) and the
maximality property introduced by Tkadlec as common generalizations of
orthocomplete and lattice effect algebras. We show that every block of an
Archimedean homogeneous effect algebra satisfying the property (W+) 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.
