A remark on QF rings
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This article mainly concentrates on the open question wheth\-er a right self-injective ring $R$ is necessary QF if $R/S_l$ is left Goldie. It is answered affirmatively under the condition $S_l\subseteq S_r$, where $S_l$ and $S_r$ denote the left socle and right socle of $R$ respectively. And the original condition ``right self-injective" can be weakened to ``right CS and right P-injective". It is also proved that a semiperfect, left and right mininjective ring $R$ is QF if $S_r\subseteq^{ess}R_R$ and $R/S_l$ is left Goldie.
Abstract
This article mainly concentrates on the open question wheth\-er a right self-injective ring $R$ is necessary QF if $R/S_l$ is left Goldie. It is answered affirmatively under the condition $S_l\subseteq S_r$, where $S_l$ and $S_r$ denote the left socle and right socle of $R$ respectively. And the original condition ``right self-injective" can be weakened to ``right CS and right P-injective". It is also proved that a semiperfect, left and right mininjective ring $R$ is QF if $S_r\subseteq^{ess}R_R$ and $R/S_l$ is left Goldie.
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