  Let $R$ be a left and right Noetherian ring and $n,k$ any non-negative
integers. $R$ is said to satisfy the Auslander-type condition $G_n(k)$ if the
right flat dimension of the $(i+1)$-st term in a minimal injective resolution
of $R_R$ is at most $i+k$ for any $0 \leq i \leq n-1$. In this paper, we prove
that $R$ is $G_n(k)$ if and only if so is a lower triangular matrix ring of any
degree $t$ over $R$.
