[1]陈 东,王芳贵*,胡 葵.G-内射模的直和与G-平坦模的直积问题[J].四川师范大学学报(自然科学版),2017,(04):486-490.[doi:10.3969/j.issn.1001-8395.2017.04.010 ]
 CHEN Dong,WANG Fanggui,HU Kui.The Problems on the Direct Sum of G-injective Modules and the Direct Product of G-flat Modules[J].Journal of SichuanNormal University,2017,(04):486-490.[doi:10.3969/j.issn.1001-8395.2017.04.010 ]
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G-内射模的直和与G-平坦模的直积问题()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2017年04期
页码:
486-490
栏目:
基础理论
出版日期:
2017-04-30

文章信息/Info

Title:
The Problems on the Direct Sum of G-injective Modules and the Direct Product of G-flat Modules
文章编号:
1001-8395(2017)04-0486-05
作者:
陈 东1 王芳贵2* 胡 葵3
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
Author(s):
CHEN Dong1 WANG Fanggui2 HU Kui3
1. College of Information Science and Engineering, Chengdu University, Chengdu 610106, Sichuan;
2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan;
3. College of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan
关键词:
G-内射模 G-平坦模 Noether环 直和 直积
Keywords:
G-injective module G-flat module Noetherian ring direct sum direct product
分类号:
O154
DOI:
10.3969/j.issn.1001-8395.2017.04.010
文献标志码:
A
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.
Abstract:
It is proved that, over Artinian rings, 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 under arbitrary direct products.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2016-12-21
基金项目:国家自然科学基金(11671283)和教育部博士点专项科研基金(20125134110002)
*通信作者简介:王芳贵(1955—),男,教授,主要从事交换代数、同调代数与代数K-理论的研究,E-mail:wangfg2004@163.com
更新日期/Last Update: 2017-04-30