Primitive group rings and Noetherian rings of quotients
Primitive group rings and Noetherian rings of quotients
Let $k$ be a field, and let $G$ be a countable nilpotent group with centre $Z$. We show that the group algebra $kG$ is primitive if and only if $k$ is countable, $G$ is torsion free, and there exists an abelian subgroup $A$ of $G$, of infinite rank, with $A …