Foxby equivalences associated to strongly Gorenstein modules

抄録

In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly _P-Gorenstein, _I-Gorenstein and _F-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left R-modules in the left Auslander class and the subcategory of strongly _P-Gorenstein left S-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.