Effect Algebras Which Can Be Covered by MV-Algebras

We exhibit effect algebras which can be covered by MV-subalgebras. We show that any effect algebra E which satisfies the Riesz interpolation property (RIP) and the so-called difference-meet property (DMP) can be covered by blocks, maximal subsets of mutually strongly compatible elements of E, which are always MV-subalegbras. This result generalizes that of Rieanová who proved the same result for lattice-ordered effect algebras. We show that for effect algebras with only (RIP) the result in question can fail.