A Note on Quasi-Frobenius Rings
| dc.creator | Shen, Liang | |
| dc.creator | Chen, Jianlong | |
| dc.date | 2005-04-05 | |
| dc.date.accessioned | 2026-07-07T05:18:47Z | |
| dc.date.available | 2026-07-07T05:18:47Z | |
| dc.description | The Faith-Menal conjecture says that every strongly right $Johns$ ring is $QF$. The conjecture is also equivalent to say every right noetherian left $FP$-injective ring is $QF$. In this short article, we show that the conjecture is true under the condition(a proper generalization of left $CS$ condition)that every nonzero complement left ideal is not small(a left ideal $I$ is called small if for every left ideal $K$, $K$+$I$=$R$ implies $K$=$R$). It is also proved that (1) $R$ is $QF$ if and only if $R$ is a left and right mininjective ring with $ACC$ on right annihilators in which $S_{r}\subseteq ^{ess}R_{R}$; (2) $R$ is $QF$ if and only if $R$ is a right simple injective ring with $ACC$ on right annihilators in which $S_{r}\subseteq ^{ess}R_{R}$. Several known results on $QF$ rings are obtained as corollaries. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504068 | |
| dc.identifier | http://arxiv.org/abs/math/0504068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74788 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16L60; 16D50 | |
| dc.title | A Note on Quasi-Frobenius Rings | |
| dc.type | text |