Separable subalgebras of a class of Azumaya algebras (Q1384236)

The author defines a \(GHS\)-extension as a \(G\)-Galois extension that is also Hirata-separable and whose fixed ring is a projective and separable \(C^G\)-algebra, where \(C\) is the center of the base ring. He proves that under the induced inner action of the group \(G\) the skew group ring \(S*G\) is a \(GHS\)-extension if and only if \(S\) is a \(G\)-Galois extension of \(S^G\) and the fixed ring is a projective and separable \(C^G\)-algebra. In this case, he shows first that any subring \(S*K\) of the skew group ring produced by subgroups \(K\) of \(G\) is a \(K\)-Galois extension whose fixed ring is a separable \(C^G\)-algebra. He proceeds by showing that in general any separable \(C^G\)-subalgebra \(T\) of a \(GHS\)-extension \(S\) is also \(NHS\)-extension, where \(N\) is the restriction to \(T\) of the inertia group of the commutator of \(T\) in \(S\).