Auslander Categories and Free Normalizing Extensions  

Auslander范畴和自由正规化扩张

作　　者：GU Qin-qin ZHUO Yuan-fan 谷勤勤;卓远帆(School of Mathematics and Physics,Anhui University of Technology,Maanshan 243032,China)

机构地区：[1]School of Mathematics and Physics,Anhui University of Technology,Maanshan 243032,China

出　　处：《Chinese Quarterly Journal of Mathematics》2021年第2期204-209,共6页数学季刊（英文版）

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

摘　　要：Let_(R)C_(S) be a semidualizing(R,S)-bimodule.Then_(R)C_(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 Hom S(_(B)B_(S),_(R)C_(S))is a semidualizing(A,B)-bimodule under some suitable conditions,and so Hom S(_(B)B_(S),_(R)C_(S))induces an equivalence between the Auslander class AHomS (_(B)B_(S),_(R)C_(S))(B). and the Bass class BHomS (BBS,RCS)(A) Furthermore,under a suitable condition on_(R)C_(S),we develop a generalized Morita theory for Auslander categories.

关 键 词：Semidualizing module Auslander class Excellent extension 

分 类 号：O154.2[理学—数学]