Self-splitting abelian groups

G is a reduced torsion-free Abelian group such that for every direct sum circle plusG of copies of G(1) Ext(circle plusG, circle plusG) = 0 if and only if G is a free module over a rank 1 ring. For every direct product Pi G of copies of G, Ext (Pi G, Pi G) = 0 if and only if G is cotorsion.