A taxonomy of 2-primal rings

Reversible and symmetric rings

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 61) 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 Σ-injective rings and Σ-CS rings

When self-injective rings are qf: a report on a problem

Basic examples and extensions of symmetric rings

We introduce the concepts of (n, d)-injective and (n, d)-flat as generalizations of injective, flat modules and homological dimensions, and use them to characterize right n-coherent rings and right (weak) (n, d)-rings in various way. Some known results can be obtained as corollaries.

On n -Coherent Rings and ( n , d )-Rings

Structure of minimal noncommutative duo rings and minimal strongly bounded non-duo rings

(1999). On n-presented modules and almost excellent extensions. Communications in Algebra: Vol. 27, No. 3, pp. 1091-1102.

Weimin Xue

Papers

Structure of minimal noncommutative duo rings and minimal strongly bounded non-duo rings

On n-presented modules and almost excellent extensions ∗

Hopfian modules and co-hopfian modules

A note on perfect self-injective rings (*)

Semiregular modules and f-semiperfect modules