On essential extensions of direct sums of either injective or projective modules - Kosan, M. Tamer; Truong Cong Quynh (World Scientific Publ Co Pte Ltd, 2014)
For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum of injective right R-modules is injective, and R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of injective right R-modules. In this paper, we prove that R is right Noetherian if and only if every essential extension of a direct sum of injective hulls of simple right R-modules is a direct sum of either injective right R-modules or projective right R-modules.
Keywords: QF-ring; Noetherian ring; locally Noetherian module