FP-Gorenstein cotorsion modules

Let R be a ring. In this paper, FP-Gorenstein cotorsion modules are introduced and studied. An R-module N is said to be FP-Gorenstein cotorsion if Ext1 R(F;N) = 0 for any finitely presented Gorenstein flat R-module F. We prove that the class of FP-Gorenstein cotorsion modules is covering and preenveloping over coherent rings. FP-Gorenstein cotorsion dimension of modules and rings are also studied. Some properties of FP-Gorenstein cotorsion modules are given.