Let $G$ be a finite group and $R=\mathbb{Z}[G]$ the integral group ring. If $G$ is such that $R$ is Noetherian (so $G$ polycyclic-by-finite) when does $R$ have finite global dimension? Another way of asking the question is, when is $R$ regular?
When does an integral group ring have finite global dimension?
4
$\begingroup$
noncommutative-algebra
noetherian
group-rings
global-dimension
regular-rings