On Galois projective group rings (Q1173913)

If \(A\) is a ring with 1 and center \(C\), and \(G\) a finite group whose order is invertible in \(A\), let \(G'\) be the inner automorphism group induced by the set of units \(\{U_ g\mid g\in G\}\) and \(A^{G'}\) the elements of A which are left fixed by each element of \(G'\). The authors show that when \(A\) is a Galois extension of \(A^{G'}\) with Galois group \(G'\) and \(\sum_ gA^{G'}U_ g\) has center \(C\), then \(A=\sum A^{G'}U_ g\). In addition they give a condition, in terms of separability, when \(A\) is a projective group ring.