Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Gorenstein injective covers and envelopes over noetherian rings


Authors: Edgar E. Enochs and Alina Iacob
Journal: Proc. Amer. Math. Soc. 143 (2015), 5-12
MSC (2010): Primary 18G25, 13D02
Published electronically: August 18, 2014
MathSciNet review: 3272726
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 18G25, 13D02

Retrieve articles in all journals with MSC (2010): 18G25, 13D02


Additional Information

Edgar E. Enochs
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Alina Iacob
Affiliation: 1209 Shasta Court, Statesboro, Georgia 30458

DOI: https://doi.org/10.1090/S0002-9939-2014-12232-5
Received by editor(s): July 9, 2012
Received by editor(s) in revised form: October 23, 2012, and February 7, 2013
Published electronically: August 18, 2014
Additional Notes: The second author has been partially supported by a Georgia Southern University Faculty Research Committee Grant.
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.