Ding modules and dimensions over formal triangular matrix rings

Let T=\bigl(\begin{smallmatrix}A&0\\U&B\end{smallmatrix}\bigr) be a formal triangular matrix ring, where A and B are rings and U is a (B, A) -bimodule. We prove: (1) If U_{A} and _{B}U have finite flat dimensions, then a left T -module \bigl(\begin{smallmatrix}M_1\\ M_2\end{smallmatrix}\bigr)_{\varphi^{M}} is Ding projective if and only if M_1 and M_2/{\operatorname{im}(\varphi^{M})} are Ding projective and the morphism \varphi^{M} is a monomorphism. (2) If T is a right coherent ring, _{B}U has finite flat dimension, U_{A} is finitely presented and has finite projective or \operatorname{FP} -injective dimension, then a right T -module (W_1, W_2)_{\varphi_{W}} is Ding injective if and only if W_1 and \ker(\widetilde{\varphi_W}) are Ding injective and the morphism \widetilde{\varphi_W} is an epimorphism. As a consequence, we describe Ding projective and Ding injective dimensions of a T -module.