@Article{CMR-28-1,
author = {Xiulan, Wang},
title = {Uniquely Strongly Clean Group Rings},
journal = {Communications in Mathematical Research },
year = {2012},
volume = {28},
number = {1},
pages = {17--25},
abstract = {<p style="text-align: justify;">A ring $R$ is called clean if every element is the sum of an idempotent and
a unit, and $R$ is called uniquely strongly clean (USC for short) if every element is
uniquely the sum of an idempotent and a unit that commute. In this article, some
conditions on a ring $R$ and a group $G$ such that $RG$ is clean are given. It is also
shown that if $G$ is a locally finite group, then the group ring $RG$ is USC if and only
if $R$ is USC, and $G$ is a 2-group. The left uniquely exchange group ring, as a middle
ring of the uniquely clean ring and the USC ring, does not possess this property, and
so does the uniquely exchange group ring.</p>},
issn = {2707-8523},
doi = {https://doi.org/2012-CMR-19061},
url = {https://global-sci.com/article/81814/uniquely-strongly-clean-group-rings}
}