Singularity categories with respect to Ding projective modules

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