Theorem

When a group ring is local

For a ring $R$ and a group $G$: If $R[G]$ is local, then $R$ is local, $R/J(R)$ has characteristic $p>0$, and $G$ is a $p$-group. The converse holds if $G$ is a locally finite group.

Reference(s)

  • G. Renault. Sur les anneaux de groupes. (1971) @ Theorem 1