Singularity categories with respect to Ding projective modules

We introduce the singularity category with respect to Ding projective modules, D bdpsg(R), as the Verdier quotient of Ding derived category D bDP(R) by triangulated subcategory K b(DP), and give some triangle equivalences. Assume DP is precovering. We show that D bDP(R) . K .,dpb(DP) and D bdpsg(R) . D bdefect(R). We prove that each R-module is of finite Ding projective dimension if and only if D bdpsg(R) = 0.