中文摘要：

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.

英文摘要：

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.