When do the Gorenstein Injective Modules and Strongly Cotorsion Modules Coincide?

For a left Noetherian ring R, if the supremum of flat dimensions of all injective left R-modules is finite, we prove that strongly cotorsion left R-modules coincide with Gorenstein injective modules. Furthermore, if idR R ∞, we describe these two classes of modules as certain right perpendiculars D⊥, where D are the classes of injective modules, modules with finite injective and flat dimension, respectively.