A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. Since
then, these classical artinian rings have continued to fascinate ring theorists with their …

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 …

设R 是交换环, 表示R 的极大理想生成的乘法系, M 是R-模. 若对R 的任何极大理想m, 有ExtR1
(R/m, M)= 0, 则M 称为极大性内射模. 若R 自身为极大性内射模, 则R 称自极大性内射环 …

Motivated by a result of Mochizuki [Mochizuki, H.(1965). Finitistic global dimension for rings.
Pacific J. Math. 15 (1): 249–258] that, for a left perfect ring R with Jacobson radical if and …

Abstract A right R–module E over a ring R is said to be maximally injective in case for any
maximal right ideal m of R, every R–homomorphism f: m→ E can be extended to an R …

环论中Faith 三大猜测(FGF 猜测, Faith-Menal 猜测和Faith 猜测) 是指右F GF-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 …

Let R be a ring with second singular right ideal and second singular left ideal. Motivated by a
result in Zhou (Zhou, Y.(2002). Rings in which certain right ideals are direct summands of …

Let R be a ring. The following results are proven. 1. If R is semilocal, right Kasch and right
simple-injective, then R is semiperfect, left and right finitely cogenerated. 2. If R is left perfect …

A ring R is called a right WPF-ring (weak PF-ring) if R is a semiperfect right simple-injective
ring with essential right socle. The class of right WPF-rings is broader than that of right PF …