具有Auslander n-Gorenstein性质的模(英文)  

Modules Admitting Auslander n-Gorenstein property

作　　者：黄宠辉[1] 王恒太[1] 

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《安徽师范大学学报（自然科学版）》2012年第4期318-321,共4页Journal of Anhui Normal University(Natural Science)

基　　金：Supported by NSFC(11101217,11126169);scientific research fund of hunan provincial education department(10C1143)

摘　　要：引入了具有Auslandern-Gorenstein性质模的概念,本文研究了具有Auslandern-Gorenstein性质的环与模的性质.给出了Auslandern-Gorenstein环的新的刻画,即:环R是Auslandern-Gorenstein环当且仅当每个有限生成Gorenstein投射模具有Auslandern-Gorenstein性质,当且仅当由全体具有Auslandern-Gorenstein性质的模组成的子范畴是反变有限resolving的.The notion of modules admitting Auslander n-Gorenstein property is introduced. This paper studies the properties of modules and rings which admit Auslander n-Gorenstein property. A new characterization of Auslander n-Gorenstein Artin algebra is given, that is, R is Auslander n- Gorenstein if and only if every Gorenstein projective module admits Auslander n-Gorenstein property if and only if the subcategory consisting of all modules admitting Auslander n-Gorenstein property is contravariantly finite and resolving.

关 键 词：Auslandern-Gorenstein性质 Auslandern-Gorenstein环 GORENSTEIN投射模 

分 类 号：O153.3[理学—数学]