Selfduality and strongly graded rings (Q1355664)

Let \(R\) be a ring graded by a finite group \(G\). The author proves that \(R\) has graded self-duality iff the smash product \(R\# G\) has self-duality iff \(R\) has self-duality. If \(R\) is strongly graded then \(R\) has self-duality iff its initial subring \(R_e\) has self-duality. He also proves that a skew group ring \(S*_\alpha G\) has self-duality iff \(S\) has self-duality.