[1]陈建龙,李文喜.环论中Faith三大猜测的进展[J].东南大学学报(自然科学版),2002,32(3):523-527.[doi:10.3969/j.issn.1001-0505.2002.03.042]
 Chen Jianlong,Li Wenxi.Developments of three Faith conjectures in ring theory[J].Journal of Southeast University (Natural Science Edition),2002,32(3):523-527.[doi:10.3969/j.issn.1001-0505.2002.03.042]
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环论中Faith三大猜测的进展()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
32
期数:
2002年第3期
页码:
523-527
栏目:
数学、物理学、力学
出版日期:
2002-05-20

文章信息/Info

Title:
Developments of three Faith conjectures in ring theory
作者:
陈建龙 李文喜
东南大学应用数学系,南京 210096
Author(s):
Chen Jianlong Li Wenxi
Department of Applied Mathematics, Southeast University, Nanjing 210096,China
关键词:
QF环 FGF-环 Johns环 FP-内射环
Keywords:
QF ring FGF ring Johns ring FP-injective ring
分类号:
O153.3
DOI:
10.3969/j.issn.1001-0505.2002.03.042
摘要:
环论中Faith三大猜测(FGF猜测、Faith-Menal猜测和Faith猜测)是指右FGF-环、强右Johns环以及左完全右内射环均为QF环.其中R是右FGF-环指任一个有限生成右R-模可嵌入自由模的环,强右Johns环是指右Norther左FP-内射环.本文介绍了Faith三大猜测的历史背景及最新进展,给出了右CF-环及右Johns环为右Artin环的条件,提出了与三大猜测有关的一些公开问题.
Abstract:
The three famous Faith-conjectures in ring theory(FGF conjecture, Faith-Menal conjecture, Faith conjecture)are that right FGF-ring, right strong Johns ring and left perfect right injective ring are all QF ring. A ring is called right FGF-ring if every finitely generated right R-module embeds in a free module; a ring is called right strong Johns ring if R is a right Noether and left FP-injective ring. In this paper, the background and latest development of the three famous conjectures in ring theory are introduced. The conditions for a right CF-ring or a right Johns ring to be right Artin ring are given and some open problems related to the three famous conjectures are proposed.

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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金资助项目(10171011)、江苏省自然科学基金资助项目(2001001).
作者简介: 陈建龙(1963—),男,教授,jlchen@seu.edu.cn.
更新日期/Last Update: 2002-05-20