On the isomorphic classes of hopf-galois extensions with normal bases over a commutative ring

In this paper we consider the isomorphic classes of H-Galois extensions with the normal basis property over a fixed commutative ring B for a finite Hopf algebra H. The result is that when H is cocommutative, then the above isomorphic classes and the 2-nd cohomology group H 2(L*, U) are isomorphic as groups under the product defined in this paper, where L=B.H, L*=Hom B (L, B).