Theorem

When a group ring is von Neumann regular

The group ring $R[G]$ is von Neumann regular if and only if $R$ is von Neumann regular and $G$ is a locally finite group such that the order of every finite subgroup of $G$ is a unit in $R$.

Reference(s)

I. G. Connell. On the group ring. (1963) @ Theorem 3 p 660