A UNIFIED APPROACH TO VARIOUS GORENSTEIN MODULES

Let V,W,Y,X be four classes of modules. In this paper, a notion of (V,W,Y,X )Gorenstein modules is introduced, which unifies a number of well-known Gorenstein modules. Under certain mild assumptions on the classes V,W,Y,X , we first study properties of (V,W,Y,X )-Gorenstein modules. Then, we apply the obtained results to establish the Foxby equivalences associate to (V,W,Y,X )-Gorenstein modules. Many results on the Gorenstein modules involved in this general setting can be obtained as corollaries.