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http://dx.doi.org/10.4134/BKMS.b150441

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.3, 2016 , pp. 925-942 More about this Journal
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.
Keywords
right ${\pi}$-duo ring; (weakly) right duo ring; (strongly) ${\pi}$-regular ring; every prime ideal is maximal; polynomial ring; matrix ring;
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Times Cited By KSCI : 3  (Citation Analysis)
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