The invariant subrings of DeMeyer-Kanzaki Galois extensions (Q1612066)

Summary: Let \(B\) be a ring with 1, \(G\) a finite automorphism group of \(B\), \(C\) the center of \(B\), and \(B^G\) the set of elements in \(B\) fixed under each element in \(G\). When \(B\) is a DeMeyer-Kanzaki Galois extension of \(B^G\) with Galois group \(G\), it was shown that a separable subring \(S\) of \(B\) over \(B^G\) is equal to \(B^K\) for some subgroup \(K\) of \(G\) if and only if \(CJ^{(S)}_g\) is a faithful \(C\)-module for each \(g\not\in K\), where \(J^{(S)}_g=\{s-g(s)\mid s\in S\}\). Moreover, the invariant subrings of \(C\) over \(C^G\) (i.e., \(S=C^K\) for some subgroup \(K\) of \(G\)) and of \(B*G\) over \((B*G)^{\overline G}\) are characterized in terms of the faithful \(B\)-module \(BJ^{(S)}_g\) and the faithful \(C^G\)-module \(C^GJ^{(S)}_g\) respectively, for \(g\in G\).