ABSTRACT
Throughout, let B be a Galois algebra over a commutative ring R with Galois group G: C the center of B, K = {g G G \ g(c) = c for each c 6 C}, Jg = {b G B \ bx = g(x)b for all x & B} for each g & G, eg a central idempotent in C such that BJg = egB ([5]), G(eg) = {g £ G g ( e g ) = eg}, Kg = {g e G \ g(egc) = egc for each egc & egC}, Bg — Y^hzK e9^h ^or eac^ 9 e ^> an<^ ^9 = {o-& A\ax = g(x)a for all x G A} for a subring A of B. We keep the definitions of a Galois extension, a Galois algebra, a central Galois algebra, a separable extension, and an Azumaya algebra as denned in ([6]). An Azumaya Galois extension A with Galois group G is a Galois extension A of AG which is a CG-Azumaya algebra where C the center of A ([!]).
