• Title/Summary/Keyword: left MC2 rings

Search Result 3, Processing Time 0.035 seconds

MC2 Rings

  • Wei, Jun-Chao
    • Kyungpook Mathematical Journal
    • /
    • v.48 no.4
    • /
    • pp.651-663
    • /
    • 2008
  • In this paper, we first study some characterizations of left MC2 rings. Next, by introducing left nil-injective modules, we discuss and generalize some well known results for a ring whose simple singular left modules are Y J-injective. Finally, as a byproduct of these results we are able to show that if R is a left MC2 left Goldie ring whose every simple singular left R-module is nil-injective and GJcp-injective, then R is a finite product of simple left Goldie rings.

On Rings Containing a Non-essential nil-Injective Maximal Left Ideal

  • Wei, Junchao;Qu, Yinchun
    • Kyungpook Mathematical Journal
    • /
    • v.52 no.2
    • /
    • pp.179-188
    • /
    • 2012
  • We investigate in this paper rings containing a non-essential $nil$-injective maximal left ideal. We show that if R is a left MC2 ring containing a non-essential $nil$-injective maximal left ideal, then R is a left $nil$-injective ring. Using this result, some known results are extended.

SOME ABELIAN MCCOY RINGS

  • Rasul Mohammadi;Ahmad Moussavi;Masoome Zahiri
    • Journal of the Korean Mathematical Society
    • /
    • v.60 no.6
    • /
    • pp.1233-1254
    • /
    • 2023
  • 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.