Abstract
By investigating the properties of some special covers and envelopes of modules, we prove that if R is a Gorenstein ring with the injective envelope of R R flat, then a left R-module is Gorenstein injective if and only if it is strongly cotorsion, and a right R-module is Gorenstein flat if and only if it is strongly torsionfree. As a consequence, we get that for an Auslander-Gorenstein ring R, a left R-module is Gorenstein injective (resp. flat) if and only if it is strongly cotorsion (resp. torsionfree).
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