Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON A GENERALIZATION OF RIGHT DUO RINGS

  • Kim, Nam Kyun (School of Basic Sciences Hanbat National University) ;
  • Kwak, Tai Keun (Department of Mathematics Daejin University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University)
  • Received : 2015.06.08
  • Published : 2016.05.31
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Abstract

We study the structure of rings whose principal right ideals contain a sort of two-sided ideals, introducing right ${\pi}$-duo as a generalization of (weakly) right duo rings. Abelian ${\pi}$-regular rings are ${\pi}$-duo, which is compared with the fact that Abelian regular rings are duo. For a right ${\pi}$-duo ring R, it is shown that every prime ideal of R is maximal if and only if R is a (strongly) ${\pi}$-regular ring with $J(R)=N_*(R)$. This result may be helpful to develop several well-known results related to pm rings (i.e., rings whose prime ideals are maximal). We also extend the right ${\pi}$-duo property to several kinds of ring which have roles in ring theory.

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