WEAK AB-CONTEXT FOR FP-INJECTIVE MODULES WITH RESPECT TO SEMIDUALIZING MODULES

Let S and R be rings and C-S(R) a semidualizing bimodule. We define and study G(C)-FP-injective R-modules, and these modules are exactly C-Gorenstein injective R-modules defined by Holm and Jorgensen provided that S = R is a commutative Noetherian ring. We mainly prove that the category of G(C)-FP-injective R-modules is a part of a weak AB-context, which is dual of weak AB-context in the terminology of Hashimoto. In particular, this allows us to deduce the existence of certain Auslander-Buchweitz approximations for R-modules with finite G(C)-FP-injective dimension. As an application, a new model structure in Mod R is given.