# Simple modules over Auslander regular rings

Authors
Type
Published Article
Journal
Open Mathematics
Publisher
De Gruyter Open
Publication Date
Dec 29, 2017
Volume
15
Issue
1
Pages
1618–1622
Identifiers
DOI: 10.1515/math-2017-0138
Source
De Gruyter
Keywords
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) $\begin{array}{} \text{Ext}_{{\it\Lambda}}^{1}(S,\ {\it\Lambda}) \end{array}$ 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.