Non-commutative separability and group actions (Q1802357)

The author considers the conditions of \(H\)-separability, strong separability and separability for noncommutative rings, in particular for skew group rings \(S * G\) over \(S\), \(G\) a finite group. He gives sufficient conditions for \(S*G\) to be strongly separable over \(S\) and necessary and sufficient conditions for \(S*G\) to be \(H\)-separable over \(S\). It is shown that if \(S*G\) is \(H\)-separable over \(S\), then \(S\) cannot be \(H\)-separable over \(R\), the fixed ring of \(S\) under a faithful action of \(G\).