A particularly rich theory is available for commutative noetherian rings due to Eben Matlis, . Every injective module is uniquely a direct sum of indecomposable injective modules, and the indecomposable injective modules are uniquely identified as the injective hulls of the quotients "R"/"P" where "P" varies over the prime spectrum of the ring. The injective hull of "R"/"P" as an "R"-module is canonically an "R""P" module, and is the "R""P"-injective hull of "R"/"P". In other words, it suffices to consider local rings. The endomorphism ring of the injective hull of "R"/"P" is the completion formula_3 of "R" at "P".