Covers of modules over a fixed ring (Q1375359)

Let \(R\) be a ring and let \(G\) be a finite group acting on \(R\) with \(1\in\text{tr}(Z(R))\), and let \(R^G\) denote the fixed ring. The authors give conditions under which the existence of relative injective covers of any module over \(R^G\) follows from the existence of relative injective covers of modules over \(R\). Similar results are proved for flat covers. In particular it is shown that if \(_{R^G}R\) is flat and every left \(R\)-module has a flat cover, then every left \(R^G\)-module has a flat cover.