The Auslander-Type Condition of Triangular Matrix Rings
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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 $R$.
13 pages
13 pages