Gorenstein injective covers and envelopes over noetherian rings

Enochs, Edgar; Iacob, Alina

doi:10.1090/S0002-9939-2014-12232-5

Gorenstein injective covers and envelopes over noetherian rings
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by Edgar E. Enochs and Alina Iacob

Proc. Amer. Math. Soc. 143 (2015), 5-12

DOI: https://doi.org/10.1090/S0002-9939-2014-12232-5

Published electronically: August 18, 2014

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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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