Ding Projective Modules and Dimensions over Formal Triangular Matrix Rings

Let T be a formal triangular matrix ring. We prove that, if for each 1 ≤ j < i ≤ n, Uij is flat on both sides, then a left T-module ■ is Ding projective if and only if M1 is a Ding projective left A1-module and for each 1 ≤ k ≤ n-1 the mapping Фk+1,k : Uk+1,k■AkMk→Mk+1 is injective with cokernel Ding projective over Ak+1. As a consequence, we describe Ding projective dimension of a left T-module.