NOTES ON STABILITY OF GORENSTEIN CATEGORIES

Let be a class of left R-modules that contains all projective left R-modules. We study a kind of stability of -Gorenstein projective modules and settle in affirmative the following question: given an exact sequence of -Gorenstein projective left R-modules G = ⋯ → G1 → G0 → G0 → G1 → ⋯ such that the complex HomR(G, F) is exact for each left R-module , is the module -Gorenstein projective? Some applications are also given.