TY - JOUR
T1 - Uniquely Strongly Clean Group Rings
AU - Wang , Xiulan
JO - Communications in Mathematical Research 
VL - 1
SP - 17
EP - 25
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19061.html
KW - clean ring, group ring, $p$-group, USC ring.
AB - <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>