Injective envelopes and flat covers of Matlis reflexive modules

AbstractWe show that for a commutative noetherian local ring R, every Matlis reflexive R-module has a reflexive injective envelope if and only if every Matlis reflexive R-module has a reflexive flat cover. This occurs if and only if R is complete and has Krull dimension less than or equal to 1. We also exhibit a family of Matlis reflexive R-modules whose injective envelopes are not Matlis reflexive