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 introduce and investigate the notion of DC-projective complexes. We first prove that a complex X is DC-projective if and only if each degree of X is a DC-projective module and Hom(X;H) is exact for any C-flat complex H. As immediate consequences of this result, some properties of DC-projective complexes are given. Secondly, we investigate a kind of stability of DC-projective complexes by showing that an iteration of the procedure used to define the DC-projective complexes yields exactly the DC-projective complexes. Finally, We introduce and characterize the notion of DC-projective dimension of complexes.