Szeto, George; Xue, Lianyong Some correspondences for a center Galois extension. (English) Zbl 1003.16017 Math. Jap. 52, No. 3, 463-468 (2000). Summary: Let \(B\) be a ring with \(1\), \(G\) a finite automorphism group of \(B\), \(C\) the center of \(B\), \(B^G\) the set of elements in \(B\) fixed under each element in \(G\). \(B*G\) a skew group ring in which the multiplication is given by \(gb=g(b)g\) for \(b\in B\) and \(g\in G\). Assume \(C\) is a Galois algebra with Galois group \(G|_C\cong G\). Two correspondence theorems are given between some sets of separable extensions in the skew group ring \(B*G\). Moreover, a necessary and sufficient condition is given for a subring \(S\) of \(B\) over \(B^G\) such that \(S=B^K\) for some subgroup \(K\) of \(G\). Consequently, a correspondence is established between the set of subgroups of \(G\) and a set of subrings of \(B\) over \(B^G\). MSC: 16S35 Twisted and skew group rings, crossed products 16W20 Automorphisms and endomorphisms 16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16W22 Actions of groups and semigroups; invariant theory (associative rings and algebras) Keywords:finite automorphism groups; centers; skew group rings; Galois algebras; Galois groups; correspondence theorems; separable extensions PDFBibTeX XMLCite \textit{G. Szeto} and \textit{L. Xue}, Math. Japon. 52, No. 3, 463--468 (2000; Zbl 1003.16017)