GORENSTEIN INJECTIVE MODULES AND ENOCHS’ CONJECTURE

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.