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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.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19061.html} }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.