[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] 点击复制 环论中Faith三大猜测的进展() 分享到： var jiathis_config = { data_track_clickback: true };

32

2002年第3期

523-527

2002-05-20

文章信息/Info

Title:
Developments of three Faith conjectures in ring theory

Author(s):
Department of Applied Mathematics, Southeast University, Nanjing 210096,China

Keywords:

O153.3
DOI:
10.3969/j.issn.1001-0505.2002.03.042

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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