The Auslander-Type Condition of Triangular Matrix Rings

Chonghui Huang; Zhaoyong Huang

paper

The Auslander-Type Condition of Triangular Matrix Rings

arXiv:0903.4515

Abstract

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