Primary group rings (Q2360069)

Summary: Let \(R\) be an associative ring with identity and let \(J(R)\) denote the Jacobson radical of \(R\). We say that \(R\) is primary if \(R/J(R)\) is simple Artinian and \(J(R)\) is nilpotent. In this paper we obtain necessary and sufficient conditions for the group ring \(RG\), where \(G\) is a nontrivial abelian group, to be primary.