Auslander范畴和自由正规化扩张

谷勤勤, 卓远帆

doi:10.13371/j.cnki.chin.q.j.m.2021.02.009

数学季刊 >

2021 , Vol. 36 >Issue 2: 204 - 209

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.02.009

Auslander范畴和自由正规化扩张

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School of Mathematics and Physics, Anhui University of Technology, Maanshan 243032, China

GU Qin-qin (1979-), female, native of Laiwu, Shandong, associate professor of Anhui University of Technology, engages in algebra; ZHUO Yuan-fan (1997-), male, native of Baoying, Jiangsu, postgraduate student of Anhui University of Technology, engages in algebra. Corresponding author: GU Qin-qin.

收稿日期: 2021-02-21

网络出版日期: 2021-04-16

基金资助

Supported by the Natural Science Foundation of Anhui Province (Grant No. 2008085QA03).

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Auslander Categories and Free Normalizing Extensions

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School of Mathematics and Physics, Anhui University of Technology, Maanshan 243032, China

Received date: 2021-02-21

Online published: 2021-04-16

Supported by

Supported by the Natural Science Foundation of Anhui Province (Grant No. 2008085QA03).

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谷勤勤, 卓远帆 . Auslander范畴和自由正规化扩张[J]. 数学季刊, 2021 , 36(2) : 204 -209 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.009

Abstract

Let _RC_S be a semidualizing (R,S)-bimodule. Then _RC_S induces an equivalent between the Auslander class A_C (S) and the Bass class B_C (R). Let A and B
be free normalizing extensions of R and S respectively. In this paper, we prove that
HomS(_BB_S,_RC_S) is a semidualizing (A,B)-bimodule under some suitable conditions,
and so HomS(_BB_S,_RC_S) induces an equivalence between the Auslander class
A_{HomS (_BB_S,_RC_S )}(B)
and the Bass class
B_{HomS (_BB_S,_RC_S )}(A).
Furthermore, under a suitable condition on _RC_S, we develop a generalized Morita theory
for Auslander categories

Key words： Semidualizing module; Auslander class; Excellent extension

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Abstract