The Tensor Product of Galois Algebras

Let A and B be R-algebras with automorphism groups G and H respectively. Denote the order of G by n and the order of H by m for some integers n and m. Assume n and m are invertible in R. Then, A R B is a Galois R-algebra with Galois group G x H if and only if A and B are Galois R-algebras with Galois groups G and H respectively. Thus an equivalent condition for a central Galois algebra in terms of the tensor product is obtained.