广西师范大学学报（自然科学版） ›› 2019, Vol. 37 ›› Issue (1): 155-164.doi: 10.16088/j.issn.1001-6600.2019.01.018

• 第二十四届全国信息检索学术会议专栏 • 上一篇    下一篇

FI-gr-内射模

刘天莉莲1, 王芳贵1*, 高增辉2   

  1. 1. 四川师范大学数学与软件科学学院,四川成都610066;
    2. 成都信息工程大学应用数学学院,四川成都610225
  • 收稿日期:2018-01-12 发布日期:2019-01-08
  • 通讯作者: 王芳贵(1955—),男,湖南衡阳人,四川师范大学教授, 博士。 E-mail:wangfg2004@163.com
  • 基金资助:
    国家自然科学基金(11671283,11571164);四川省应用基础研究项目(2017JY0131)

FI-gr-injective Modules

LIU-TIAN Lilian1 , WANG Fanggui1*, GAO Zenghui2   

  1. 1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu Sichuan 610066, China;
    2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu Sichuan 610225, China
  • Received:2018-01-12 Published:2019-01-08

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摘要： 本文引入了FI-gr-内射模及强FI-gr-内射模的概念,并说明它们与分次内射模之间的相互关系。证明了分次环R是分次QF环当且仅当每个分次模是强FI-gr-内射模;设R为左分次凝聚环, 则l.FP-gr-dim(R)≤1当且仅当每个FI-gr-内射模是分次内射模。此外,还证明了l.gr-fiD(R)=sup{gr-pd(L)|L为FP-gr-内射模}。

关键词: FI-gr-内射模, 强FI-gr-内射模, FI-gr-内射维数, FP-gr-内射模

Abstract: In this paper, the notions of FI-gr-injective modules and strongly FI-gr-injective modules are introduced, and the relationship between them and graded injective modules is explained. It is proved that the graded ring R is a gr-QF ring if and only if each graded module is a strongly FI-gr-injective module; suppose R is a left gr-coherent ring, then l.FP-gr-dim(R)≤1 if and only if each FI-gr-injective module is a graded injective module. In addition, it is also proved that l.gr-fiD(R)=sup{gr-pd(L)|L is an FP-gr-injective module}.

Key words: FI-gr-injective modules, strongly FI-gr-injective modules, FI-gr-injective dimensions, FP-gr-injective modules

中图分类号: 

  • O154
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