The class of Gorenstein injective modules is covering if and only if it is closed under direct limits
Abstract
We prove that the class of Gorenstein injective modules is covering if and only if it is closed under direct limits. This adds to the list of examples that support Enochs conjecture: Every covering class of modules is closed under direct limits. We also show that the class of Gorenstein injective left R-modules is covering if and only if R is left noetherian, and such that character modules of Gorenstein injective left R modules are Gorenstein flat.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.02493
- arXiv:
- arXiv:2403.02493
- Bibcode:
- 2024arXiv240302493I
- Keywords:
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- Mathematics - Commutative Algebra
- E-Print:
- arXiv admin note: text overlap with arXiv:1512.05999 by other authors