An embedding theorem for rings

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(?₁,?₂) must be an Artinian and Noet. i.ian End(?₁) module where _i. is the injective hull of ?_i. This leads to a study of universally cotorsionless modules.