Article
Gorenstein Injective Envelopes and Covers Over Two Sided Noetherian Rings
Communications in Algebra
(2017)
Abstract
We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the connection between the Gorenstein injective modules and the strongly cotorsion modules. We prove that when the ring R is commutative noetherian of finite Krull dimension, the class of Gorenstein injective modules coincides with that of strongly cotorsion modules if and only if the ring R is in fact Gorenstein.
Keywords
- Gorenstein injective cover,
- Gorenstein injective envelope,
- Gorenstein injective module,
- Strongly cotorsion module
Disciplines
Publication Date
2017
DOI
10.1080/00927872.2016.1233193
Publisher Statement
This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the author must have permission to distribute the work or the work must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Communications in Algebra.
Citation Information
Alina Iacob. "Gorenstein Injective Envelopes and Covers Over Two Sided Noetherian Rings" Communications in Algebra Vol. 45 Iss. 5 (2017) p. 2238 - 2244 ISSN: 1532-4125 Available at: http://works.bepress.com/alina_iacob/50/