Theorem

Maschke's Theorem (on when a group algebra is semisimple.)

For any ring $R$ and group $G$, the group ring $R[G]$ is semisimple iff $R$ is semisimple and $|G|$ is a unit in $R$.

Link: https://en.wikipedia.org/wiki/Maschke%27s_theorem

Reference(s)

  • T. Lam. A first course in noncommutative rings. (2013) @ Theorem 6.1 p 80