Ding projective modules and dimensions over formal triangular matrix rings

Abstract:

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