Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weakly Semicommutative Rings and Strongly Regular Rings

  • Wang, Long (School of Mathematics, Yangzhou University, Department of Mathematics, Southeast University) ;
  • Wei, Junchao (School of Mathematics, Yangzhou University)
  • Received : 2012.02.21
  • Accepted : 2013.11.16
  • Published : 2014.03.23
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Abstract

A ring R is called weakly semicommutative ring if for any a, $b{\in}R^*$ = R\{0} with ab = 0, there exists $n{\geq}1$ such that either an $a^n{\neq}0$ and $a^nRb=0$ or $b^n{\neq}0$ and $aRb^n=0$. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if R is a left SF-ring and weakly semicommutative ring.

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References

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