WHEN SELF-INJECTIVE RINGS ARE QF: A REPORT ON A PROBLEM

被引：35

作者：

Faith, Carl ^{[1
]}

Dinh Van Huynh ^{[2
]}

机构：

[1] 199 Longview Dr, Princeton, NJ 08540 USA

[2] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2002年 / 1卷 / 01期

关键词：

Quasi-Frobenius (= QF); Pseudo-Frobenius (= PF); Finitely PF (= FPF); Self-injective; FP-injective; Continuous; annihilators; Duality; finitely generated modules embeddable in free modules (= FGF);

D O I：

10.1142/S0219498802000070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or two-sided perfect rings remains open, even assuming that the ring is semiprimary. The latter version of the problem is known as Faith's Conjecture (FC). We survey results on QF rings, especially those obtained in connection with FC. We also review various results that provide partial answers to another problem of Faith: Is a right FGF ring necessarily QF? On this topic, we provide a new result, namely that if all factor rings of R are right FGF, then R is QF (Theorem 6.1). In Sec. 7 we review results concerning the question of when a D-ring is QF. Sections 8 and 9 are devoted respectively to IF rings, and to Sigma-injective rings and Sigma-CS rings.

引用

页码：75 / 105

页数：31

共 134 条

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