SOME NOTES ON THE STRUCTURE OF GALOIS ALGEBRAS

George Szeto (U. S. A.) and Lianyong Xue (U. S. A.)

Abstract

Let B be a Galois algebra over a commutative ring R with Galois group G. Then B is a direct sum of Galois algebras such that each direct summand is a composition of a central Galois algebra and a commutative Galois algebra. A sufficient condition is also given under which B is commutative.

Keywords and phrases: Galois extensions, Galois algebras, central Galois algebras.