An element $a$ of $R$ is called s-weakly regular (SWR) if $a\in aRa^2R$. A ring $R$ is called an almost SWR if for any $a\in R$, either $a$ or $1-a$ is SWR. In this paper, we introduce almost SWR rings as the generalization of abelian von Neumann local (VNL) rings and SWR rings. We provide various properties and characterizations of almost SWR rings. We discuss various extension rings to be almost SWR. Further, we discuss SWR group rings and almost SWR group rings.
Strongly regular rings, VNL-rings, s-weakly regular rings, almost s-weakly regular rings, group rings
JANGRA, KANCHAN and UDAR, DINESH
"On almost s-weakly regular rings,"
Turkish Journal of Mathematics: Vol. 46:
5, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss5/19