Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Generalizations of V-rings

  • Song, Xianmei (Department of Mathematics, Southeast University, Department of Mathematics, Anhui Normal University) ;
  • Yin, Xiaobin (Department of Mathematics, Anhui Normal University)
  • Received : 2004.03.11
  • Published : 2005.09.23
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Abstract

In this paper, we introduce a new notion which we call a generalized weakly ideal. We also investigate characterizations of strongly regular rings with the condition that every maximal left ideal is a generalized weakly ideal. It is proved that R is a strongly regular ring if and only if R is a left GP-V-ring whose every maximal left (right) ideal is a generalized weakly ideal. Furthermore, if R is a left SGPF ring, and every maximal left (right) ideal is a generalized weakly ideal, it is shown that R/J(R) is strongly regular. Several known results are improved and extended.

Keywords

Acknowledgement

Supported by : NNSF of China, Anhui Normal University, Education Committee of Anhui Province

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