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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) $\begin{array}{c}{\text{Ext}}_{\Lambda }^1(S,\Lambda )\end{array}$ 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.