Gorenstein injective covers and envelopes over noetherian rings

Edgar E. Enochs; Alina Iacob

doi:10.1090/s0002-9939-2014-12232-5

Gorenstein injective covers and envelopes over noetherian rings

Edgar E. Enochs, Alina Iacob

Mathematical Sciences

University of Kentucky

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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.

Original language	English
Pages (from-to)	5-12
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	1
DOIs	https://doi.org/10.1090/s0002-9939-2014-12232-5
State	Published - Jan 1 2015

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Gorenstein injective covers and envelopes over noetherian rings

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