G_C-平坦模的性质的研究(英文)  

Some properties of G_C-flat modules

作　　者：谷勤勤[1] 

机构地区：[1]安徽工业大学数理学院,安徽马鞍山243032

出　　处：《安徽大学学报（自然科学版）》2012年第4期30-36,共7页Journal of Anhui University(Natural Science Edition)

基　　金：Supported by National Natural Science Foundation(10971090);Youth Foundation of Anhui University of Technology(QZ201016)

摘　　要：对于半对偶模C,研究了C-平坦模类和C-内射模类的性质,利用Bass类跟Auslander类证明了C-内射预包和C-平坦预覆盖的存在性.并将GC-平坦模的概念推广到一般环,给出了GC-平坦模的一些刻画及GC-平坦模与Auslander类的关系.Firstly, we investigated the properties of C- flat modules and C- injective modules for a semidualizing module C. Let R be a ring. Using Auslander class Ac（R） and Bass class Bc（ R）, we characterized the C-fiat precover and C- injective preenvelope of a module. Secondly, we extended the notion of the Gc -flat module to the setting of the non-noetherian ring. We gave some properties of Gc -flat modules, and obtained some relations between Gc - flat modules and the Auslander class with respect to the semidualizing module C.

关 键 词：GC-平坦 C-平坦 C-内射 

分 类 号：O154.2[理学—数学]