On central commutator Galois extensions of rings
Let \(B\) be a ring with identity, \(G\) a finite automorphism group of \(B\) of order \(n\) for some integer \(n\), \(B^G\) the set of elements in \(B\) fixed under each element in \(G\), and \(\Delta=V_B(B^G)\) the commutator subring of \(B^G\) in \(B\). Let \(A\) be a subring of \(B\). The ring \(B\) is called an \(H\)-separable extension of \(A\) if \(B\times_AB\) is isomorphic to a direct summand of a finite direct sum of \(B\) as a \(B\)-bimodule. \(B\) is called a central commutator Galois extension of \(B^G\) if \(\Delta\) is a central Galois algebra with Galois group \(G|_C\cong G\). The authors give several characterizations of a central commutator Galois extension. Also, the authors show that when \(G\) is inner, \(B\) is a central commutator Galois extension of \(B^G\) if and only if \(B\) is an \(H\)-separable projective group ring \(B^GG_f\).
scientific article; zbMATH DE number 1533308