Gorenstein Homological Properties With Respect To A Semidualizing Module C

Recently,the study of semidualizing modules and their related classes of mod-ules has attracted extensive attention of scholars.Based on many previous work of predecessors,in this thesis,we study mainly Gorenstein homological properties with respect to a semidualizing module.Let A be an abelian category with enough projective objects,X a precovering subcategory of A such that it contains all projective objects and is closed under kernels of epimorphisms and direct summands.In chapter 2,we prove that the bounded derived category D~b(A)of A can be described as certain a triangulated quotient category of homotopy categories with respect to X.Note that the Auslan-der class and its right orthogonal class with respect to a semidualizing R-module C over a commutative ring R form a complete and hereditary cotorsion pair.As an application of the above result,we show that the bounded derived category D~b(R)has a description related to the Auslander class.In chapter 3,we investigate the transfer properties of C-Gorenstein flat modules along ring homomorphisms and prove that if R is a coherent ring,S is a faithfully flat R-algebra such that the class of C(?)RS-Gorenstein flat S-modules is closed under extensions,then an R-module M is C-Gorenstein flat if and only if the S-module S(?)R M is C(?)R S-Gorenstein flat.