Quasi-unit regularity and $QB$-rings

• Date: 2012
• Main Authors: Li, Jianghua, Shangping, Wang, Xiaoqin, Shen, Xiaoqing, Sun, Лі, Їангуа, Шанґпінг, Ванг, Сяоцин, Шен, Сяоцин, Сун
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2586
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Some relations for quasiunit regular rings and $QB$-rings, as well as for pseudounit regular rings and $QB_{\infty}$-rings, are obtained. In the first part of the paper, we prove that (an exchange ring $R$ is a $QB$-ring) (whenever $x \in R$ is regular, there exists a quasiunit regular element $w \...