It is a well-known result that the direct sum of any family of injective modules over a Noetherian ring is injective. Conversely, ifAis a ring with the property that the direct sum of any family of injective modules is injective H. Bass [1] has shown thatAis Noetherian. The object of the present paper is to give necessary and sufficient conditions for the direct sum of a given family of modules over an arbitrary ring to be injective.