On essential extensions of direct sums of injective modules
A well-known theorem by Matlis and Papp says that a ring \(R\) is right Noetherian if and only if the direct sum of any collection of injective right \(R\)-modules is injective. In this paper the authors give a nice generalization of this theorem by proving that a ring \(R\) is right Noetherian if and only if any essential extension of the direct sum of any family of injective right \(R\)-modules is a direct sum of injective modules.
scientific article; zbMATH DE number 1742826