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
Recommended Citation
Belshoff, Richard G., and Jinzhong Xu. "Injective envelopes and flat covers of Matlis reflexive modules." Journal of pure and applied algebra 79, no. 3 (1992): 205-215.
Journal Title
Journal of Pure and Applied Algebra
COinS
