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We prove that the class of Gorenstein injective modules is both envelopingand covering over a two sided noetherian ring such that the character modulesof Gorenstein injective modules are Gorenstein flat. In the second part of thepaper we consider the connection between the Gorenstein injective modules andthe strongly cotorsion modules. We prove that when the ring R is commutativenoetherian of finite Krull dimension, the class of Gorenstein injective modulescoincides with that of strongly cotorsion modules if and only if the ring R isin fact Gorenstein.

Gorenstein injective envelopes and covers over two sided noetherian rings