Gorenstein χ-injective Modules With Respect To Semidualizing Modules

Let S and R be rings,SCR a faithfully semidualizing bimodule and X a class of left S-modules.As a unified generalization of GC-injective left R-modules,GC-FP-injective left R-modules and GC-weak injective left R-modules,in this thesis,we introduce the notion of GC--injective modules.Under the condition that X satisfies certain hypothesis,some properties and some equivalent characterizations of Gc-χ-injective modules are investigated and Foxby equivalences associated to some related classes of modules are established.We also show that the triple(gCχI(R),cores XICxp(R),XZCxp(R))is a weak co-AB context,where gCχI(R)(resp.,coresχICxp(R),XICxp(R))is the class of GC-χ-injective left R-modules(the class of left R-modules with finite C-χ-injective C-χ-projective dimension,the class of C-χ-injective C-χ-projective left R-modules).As an application,a new model structure in Mod S is given.