@article{Li_Shangping_Xiaoqin_Xiaoqing_2012, title={Quasi-unit regularity and $QB$-rings}, volume={64}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2586}, abstractNote={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 $w \in R$ such that $x = xyx = xyw$ for some $y \in R$) — (whenever $aR + bR = dR$ in $R$, there exists a quasiunit regular element $w \in R$ such that $a + bz = dw$ for some $z \in R$). Similarly, we also give necessary and sufficient conditions for $QB_{\infty}$-rings in the second part of the paper.}, number={3}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Li, Jianghua and Shangping, Wang and Xiaoqin, Shen and Xiaoqing, Sun}, year={2012}, month={Mar.}, pages={415-425} }