Bulletin of the Korean Mathematical Society (대한수학회보)

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A REMARK ON QF RINGS

  • Feng, Feng (School of Mathematics Southeast University) ;
  • Shen, Liang (School of Mathematics Southeast University)
  • Received : 2018.02.24
  • Accepted : 2018.10.29
  • Published : 2019.01.31
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Abstract

This article mainly concentrates on the open question whether 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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References

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