Simple modules over Auslander regular rings - Huang Chonghui; Zheng Lijing (Open Mathematics, 2017)
In this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of ExtΛ1(S,Λ)$\begin{array}{} \text{Ext}_{{\itΛ}}^{1}(S,\ {\itΛ}) \end{array} $ is equal to 1 for any simple Λ-module S with gr S = 1. As a result, we give some equivalent characterization of diagonal Auslander regular rings.