ON A GENERALIZATION OF RIGHT DUO RINGS

被引：8

作者：

Kim, Nam Kyun ^{[1
]}

Kwak, Tai Keun ^{[2
]}

Lee, Yang ^{[3
]}

机构：

[1] Hanbat Natl Univ, Sch Basic Sci, Daejeon 34158, South Korea

[2] Daejin Univ, Dept Math, Pochon 11159, South Korea

[3] Pusan Natl Univ, Dept Math Educ, Pusan 46241, South Korea

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2016年 / 53卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

right pi-duo ring; (weakly) right duo ring; (strongly) pi-regular ring; every prime ideal is maximal; polynomial ring; matrix ring;

D O I：

10.4134/BKMS.b150441

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：925 / 942

页数：18

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