Quasi-unit regularity and $QB$-rings

  • Jianghua Li School Sci., Xi’an Univ. Technology, China
  • Wang Shangping School Sci., Xi’an Univ. Technology, China
  • Shen Xiaoqin School Sci., Xi’an Univ. Technology, China
  • Sun Xiaoqing School Sci., Xi’an Univ. Technology, China

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.
Published
25.03.2012
How to Cite
LiJ., ShangpingW., XiaoqinS., and XiaoqingS. “Quasi-Unit Regularity and $QB$-Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 3, Mar. 2012, pp. 415-2, http://umj.imath.kiev.ua/index.php/umj/article/view/2586.
Section
Research articles