@article{Udar_Sharma_Srivastava_2020, title={Strongly $P$ -clean and semi-Boolean group rings}, volume={71}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2289}, abstractNote={<p>A ring $R$ is called clean (resp., uniquely clean) if every element is (uniquely represented as) the sum of an idempotent and a unit. <br>A ring $R$ is called strongly P-clean if every its element can be written as the sum of an idempotent and a strongly nilpotent element that commute. <br>The class of strongly P-clean rings is a subclass of classes of semi-Boolean and strongly nil clean rings. <br>A ring $R$ is called semi-Boolean if $R/J(R)$ is Boolean and idempotents lift modulo $J(R),$ where $J(R)$ denotes the Jacobson radical of $R.$ <br>The class of semi-Boolean rings lies strictly between the classes of uniquely clean and clean rings. <br>We obtain a complete characterization of strongly P-clean group rings. <br>It is proved that the group ring $RG$ is strongly P-clean if and only if $R$ is strongly P-clean and $G$ is a locally finite 2-group. Further, we also study semi-Boolean group rings. <br>It is proved that if a group ring $RG$ is semi-Boolean, then $R$ is a semi-Boolean ring and $G$ is a 2-group and that the converse assertion is true if $G$ is locally finite and solvable, or an FC group.</p> <p><br><br></p>}, number={12}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Udar, D. and Sharma, R. K. and Srivastava, J. B.}, year={2020}, month={Jan.}, pages={1717-1722} }