Gorenstein injective covers and envelopes over noetherian rings
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- by Edgar E. Enochs and Alina Iacob PDF
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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.
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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
- MR Author ID: 763457
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 5-12
- MSC (2010): Primary 18G25, 13D02
- DOI: https://doi.org/10.1090/S0002-9939-2014-12232-5
- MathSciNet review: 3272726