Related Module Classes With Respect To Semidualizing Modules

In this thesis, we consider the properties of the related module classes with respect to the semidualizing modules and the relative homological dimensions of these modules.Chapter1, we give some basic definitions and some needed properties.Chapter2, we investigate the C-FP-injective modules and C-flat modules. We give some characterizations of right coherent rings, left perfect rings and left Noether rings by the C-FP-injective modules and C-flat modules. We discuss when we have a(n) monic (or epic) C-flat preenvelope? Meanwhile, we characterize the left and right TC(R)-dimensions over a left Noether ring by the left derived functor of Homr(-,-).Chapter3, we introduce the concepts of the C-FP-projective and C-FP-injective C-FP-projective modules, and discuss their basic properties and dimen-sions.Chapter4, we consider the properties of the C-(n, d)-injective and C-(n, d)-flat module, and discuss the relative homological dimensions of these modules when SCR is equal to RRR. We characterize the left and right In,d-dimensions over a left n-coherent ring by the left derived functor of HomR(-,-). Meanwhile, we characterize the right In,d-dimensions and the right Fn,d-dimensions over a left n-coherent ring by the right derived functor of-(?)R-...