G-内射模的直和与G-平坦模的直积问题  

The Problems on the Direct Sum of G-injective Modules and the Direct Product of G-flat Modules

作　　者：陈东[1] 王芳贵[2] 胡葵[3] 

机构地区：[1]成都大学信息科学与工程学院,四川成都610106 [2]四川师范大学数学与软件科学学院,四川成都610066 [3]西南科技大学理学院,四川绵阳621010

出　　处：《四川师范大学学报（自然科学版）》2017年第4期486-490,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11671283);教育部博士点专项科研基金(20125134110002)

摘　　要：证明在Artin环上,G-内射模的直和是G-内射模,G-平坦模的直积是G-平坦模.进一步证明在Noether环R上,若每个R-模的G-内射维数有限,则G-内射模关于直和封闭;在凝聚环R上,若每个R-模的G-平坦维数有限,则G-平坦模关于直积封闭.It is proved that, over Artinian tings, the direct sum of Gorenstein injective modules is still Gorenstein injective and the direct product of Gorenstein flat modules is still Gorenstein flat. Moreover, it is proved that, if R is a noetherian ring on which every R-module has finite Gorenstein injective dimension, the class of Gorenstein injective modules is closed under arbitrary direct sums, and if R is a coherent ring on which every R-module has finite Gorenstein flat dimension, the class of Gorenstein flat modules is closed un- der arbitrary direct products.

关 键 词：G-内射模 G-平坦模 NOETHER环 直和 直积 

分 类 号：O154[理学—数学]