Hi! I tried to show the following but i failed: We have a finite galois extension with commutative galois group and the ring of algebraic integers in L. Suppose there exists so that the set Gal( forms a -Basis of .

Then for every field there also exists so that Gal( forms a -Basis of .

I could show that is normal and hence each Gal is just a restriction of Gal . But i dont know how to continue the argument. Can anybody please help me?

Greetings

Banach