ON HIRATA SEPARABLE GALOIS EXTENSIONS

Let B be a Hirata separable and Galois extension of B G with Galois group G of order n invertible in B for some integer n, C the center of B, and VB(B G ) the commutator subring of B G in B. It is shown that there exist subgroups K and N of G such that K is a normal subgroup of N and one of the following three cases holds: (i) VB(B K ) is a central Galois algebra over C with Galois group K, (ii) VB(B K )i s separable C-algebra with an automorphism group induced by and isomorphic with K, and (iii) B K is a central algebra over VB(B K ) and a Hirata separable Galois extension of B N with Galois group N/K. More characterizations for a central Galois algebra VB(B K ) are given.