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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
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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?)

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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

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.

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