Geodesic
Gorenstein injective modules and Enochs' conjecture
Alina Iacob1 ; Alina Iacob
1Department of Mathematical Sciences, Georgia Southern University, Statesboro (GA), USA
Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 4, pp. 197-204 
Alina Iacob; Alina Iacob. Gorenstein injective modules and Enochs' conjecture. Acta mathematica Universitatis Comenianae, Tome 93 (2024) no. 4, pp. 197-204. http://geodesic.mathdoc.fr/item/AMUC_2024_93_4_a1/
@article{AMUC_2024_93_4_a1,
     author = {Alina Iacob and Alina Iacob},
     title = { Gorenstein injective modules and {Enochs'} conjecture},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {197--204},
     year = {2024},
     volume = {93},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2024_93_4_a1/}
}
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Voir la notice de l'article provenant de la source Comenius University

We prove that the class of Gorenstein injective modules, GI, is special precovering if and only if it 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 give a characterization of the rings for which GI is covering: 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.