Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SOME ABELIAN MCCOY RINGS

  • Rasul Mohammadi (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University) ;
  • Ahmad Moussavi (Department of Pure Mathematics Faculty of Mathematical Sciences Tarbiat Modares University) ;
  • Masoome Zahiri (Department of Pure Mathematics Faculty of Mathematical Sciences Eqlid University)
  • Received : 2022.12.20
  • Accepted : 2023.09.01
  • Published : 2023.11.01
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Abstract

We introduce two subclasses of abelian McCoy rings, so-called π-CN-rings and π-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as 2-primal rings, bounded rings etc. It is shown that a ring R is π-CN whenever every nilpotent element of index 2 in R is central. These rings naturally generalize the long-known class of CN-rings, introduced by Drazin [9]. It is proved that π-CN-rings are abelian, McCoy and 2-primal. We also show that, π-duo rings are strongly McCoy and abelian and also they are strongly right AB. If R is π-duo, then R[x] has property (A). If R is π-duo and it is either right weakly continuous or every prime ideal of R is maximal, then R has property (A). A π-duo ring R is left perfect if and only if R contains no infinite set of orthogonal idempotents and every left R-module has a maximal submodule. Our achieved results substantially improve many existing results.

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References

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