Gorenstein Flat Preenvelopes

We consider a two sided noetherian ring R such that the character modules of Gorenstein injective leftR-modules are Gorenstein flat right R-modules. We then prove that the class of Gorenstein flat right R-modules is preenveloping. We also show that the class of Gorenstein flat complexes of right R-modules is preenevloping in Ch(R). In the second part of the paper we give examples of rings with t he property that the character modules of Gorenstein injective modules are G or nstein flat. We prove that any two sided noetherian ring R with i.d.Rop R < 1 has the desired property. We also prove that ifR is a two sided noetherian ring with a dualizing bimodule RVR and such thatR is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein flat .