TY - JOUR
AU - Jianghua Li
AU - Wang Shangping
AU - Shen Xiaoqin
AU - Sun Xiaoqing
PY - 2012/03/25
Y2 - 2023/12/01
TI - Quasi-unit regularity and $QB$-rings
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 64
IS - 3
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2586
AB - 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.
ER -