Kaplansky [2] proved that if P is a projective module, then every f.g. submodule of P is contained in a finitely generated direct summand iff P is the direct sum of f.g. projectives. We show that in order that all injectives have the dual property to the above statement,, for ach pair of simples (S1, S2), Hom(Ŝ1,Ŝ2) must be an Artinian and Noet. i.ian End(Ŝ1) module wherei. is the injective hull of Ŝi. This leads to a study of universally cotorsionless modules.