… class PC of C-projective modules and the class GPC of GC -projective modules, which we
use … A finitely generated module that is projective or C-projective is totally C-reflexive. Let GC …

… projective resolution of a module M is a projective resolution P of M such that each Pi is a
finitely generated projective module… AddS C is just the class of C -projective modules in Mod S. …

… b (P) is the bounded homotopy category of projective left R-modules. Let R be a commutative
Noetherian ring. Following [15], a finitely generated Rmodule C is semidualizing if the …

… section on finitely generated modules, although … projective R-module as we did with M.
Indeed, since R is noetherian and P0 is finitely generated, the submodule M1 ⊆ P0 is also finitely …

… -projective and the ℐ C -injective dimensions of a module in the noncommutative case,
weakening the condition of C being semidualizing. … , as in the case of semidualizing modules [4], …

… Throughout the paper, R is a commutative semiperfect Noetherian ring with identity and all
R-modules are finitely … The class of C-projective modules is defined as PC = {P ⊗RC | P is …

… A finitely generated R-module C is semidualizing if the natural homothety map R −→HomR(C,
C) … For example a finitely generated projective R-module of rank 1 is semidualizing. If R is …

… Auslander and Bridger in [1], introduced the notion of so-called G-dimension for finitely
generated modules over commutative Noetherian rings. Enochs and Jenda defined in [4] a …

… A finitely generated ft-module C is semidualizing if the homothety map R —> Homfl(C, C)
is an isomorphism and Ext^(C, C) = 0 for each integer i > 0. For example, R is always …

… of DC projective modules over commutative rings, where C is a semidualizing module. This
extends Gillespie and Ding, Mao’s notion of Ding projective modules. The properties of DC -…