Let R be an associative ring with identity. R is said to be semilocal if R/J(R) is (semisimple) Artinian, where J(R) denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions ...Let R be an associative ring with identity. R is said to be semilocal if R/J(R) is (semisimple) Artinian, where J(R) denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.展开更多
基金Foundation item:The NNSF(10571026)of China,the NSF(BK2005207)of Jiangsu Provincethe Specialized Research Fund(20060286006)for the Doctoral Program of Higher Education.
文摘Let R be an associative ring with identity. R is said to be semilocal if R/J(R) is (semisimple) Artinian, where J(R) denotes the Jacobson radical of R. In this paper, we give necessary and sufficient conditions for the group ring RG to be semilocal, where G is a locally finite nilpotent group.