Ding Projective Complexes With Respect To A Semidualizing Module

Let R be a commutative ring and C a semidualizing?R-module. In this article, we investigate D_C-projective complexes and the D_C-projective dimension of com-plexes. First of all, we prove that a complex X is D_C-projective if and only if the module in each degree of X is D_C-projective module and Hom(X,H) is exact for any C-flat complex H. As applications, the stability of D_C-projective complexes and D_C-projective modules are explorled. Secondly, we introduce and characterize the D_C-projective dimension of complexes.