Primary group rings

Abstract

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.