2018
Том 70
№ 7

# Quasi-unit regularity and $QB$-rings

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 3, pp 470-483.

Citation Example: Li Jianghua, Shangping Wang, Xiaoqin Shen, Xiaoqing Sun Quasi-unit regularity and $QB$-rings // Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 415-425.

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