Cartan-Eilenberg Ding projective complexes

In this article, Cartan-Eilenberg Ding projective complexes are introduced and investigated. It is shown that a complex $C$ is Cartan-Eilenberg Ding projective if and only if $C_n$ and $C_n/\mathrm{B}_n(C)$ are Ding projective in $R$-$\mathrm{Mod}$ for each $n\in\mathbb{Z}$ when $R$ is a Ding-Chen ring. Some applications are also given.