[1]谢雅静,王芳贵*,吴小英.分次投射盖和交换分次完全环[J].四川师范大学学报(自然科学版),2019,(06):729-738.[doi:10.3969/j.issn.1001-8395.2019.06.003]
 XIE Yajing,WANG Fanggui,WU Xiaoying.Graded Projective Covers and Commutative Graded Perfect Rings[J].Journal of SichuanNormal University,2019,(06):729-738.[doi:10.3969/j.issn.1001-8395.2019.06.003]
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分次投射盖和交换分次完全环()
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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:
2019年06期
页码:
729-738
栏目:
基础理论
出版日期:
2019-11-04

文章信息/Info

Title:
Graded Projective Covers and Commutative Graded Perfect Rings
文章编号:
1001-8395(2019)06-0729-10
作者:
谢雅静 王芳贵* 吴小英
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
XIE Yajing WANG Fanggui WU Xiaoying
College of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
分次多余子模 分次投射盖 分次半完全环 分次完全环
Keywords:
graded superfluous submodules graded projective covers graded semiperfect rings graded perfect rings
分类号:
O153.3; O154
DOI:
10.3969/j.issn.1001-8395.2019.06.003
文献标志码:
A
摘要:
设G是交换群,R=σ∈GRσ是交换G-分次环.给出了交换分次半完全环与分次完全环的一些等价刻画.证明:1)分次局部环上任何有限生成分次模有分次投射盖.2)R是分次半完全环当且仅当R是有限个分次局部环的直积.3)R是分次完全环当且仅当R/Jg(R)是分次半单环,且每个非零分次模都有极大分次子模; 当且仅当每个分次模有关于分次循环子模的降链条件; 当且仅当R是分次局部环Ri的直积,且每个Jg(Ri)是T-幂零的.4)若R是强分次环,则R是分次完全环当且仅当Re是完全环.
Abstract:
Let G be a commutative group and let R=σ∈GRσ be a commutative graded ring.In this paper, the equivalent characterizations about graded semiperfect rings and graded perfect rings are given.It is shown that: 1)Every finitely generated graded module over a graded local ring has a graded projective cover.2)R is graded semiperfect if and only if R is a direct product of finite graded local rings.3)R is graded perfect if and only if R/Jg(R) is graded semisimple and every nonzero graded module has a maximal graded submodule; if and only if every graded module satisfies the descending chain condition on cyclic submodules; if and only if R is a direct product of graded local rings Ri, and Jg(Ri) is a T-nilpotent ideal.4)If R is a strongly graded ring, then R is a graded perfect ring if and only if Re is a graded perfect ring if and only if a perfect ring.

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备注/Memo

备注/Memo:
收稿日期:2018-01-12 接受日期:2018-03-27 基金项目:国家自然科学基金(11671283) *通信作者简介:王芳贵(1955—),男,博士,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: 2019-11-04