#### Title

Gorenstein Injective Covers and Envelopes over Noetherian Rings

#### Document Type

Conference Proceeding

#### Publication Date

8-18-2014

#### Publication Title

Proceedings of the American Mathematical Society (AMS)

#### DOI

10.1090/S0002-9939-2014-12232-5

#### ISSN

1088-6826

#### Abstract

We prove that if* R* is a commutative Noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat, then the class of Gorenstein injective modules is closed under direct limits and it is covering.

We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative Noetherian rings with dualizing complexes.

#### Recommended Citation

Iacob, Alina, Edgar E. Enochs.
2014.
"Gorenstein Injective Covers and Envelopes over Noetherian Rings."
*Proceedings of the American Mathematical Society (AMS)*, 143: 5-12: American Mathematical Society (AMS).
doi: 10.1090/S0002-9939-2014-12232-5

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/81