Injective envelopes and flat covers of Matlis reflexive modules

Abstract

We 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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1016/0022-4049(92)90050-p

Publication Date

1992

Journal Title

Journal of Pure and Applied Algebra

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