On characterizations of a center Galois extension (Q1578978)

Let \(B\) be a ring with identity, \(C\) the center of \(B\), \(G\) a finite automorphism group of \(B\) and \(B^G\) the set of elements in \(B\) fixed under each element in \(G\). The main result established by the authors is: \(B\) is a center Galois extension of \(B^G\) (that is, \(C\) is a Galois algebra over \(C^G\) with Galois group \(G|_C\cong G\)) if and only if the ideal of \(B\) generated by \(\{c-g(c)\mid c\in C\}\) is \(B\) for each \(g\neq 1\) in \(G\).