Galois extension, algebraic closure
Let be any finite extension and let . Let be a Galois extension of containing and let be the subgroup corresponding to . Define the norm of from to to be , where the product is taken over all the embeddings of into an algebraic closure of (so over a set of coset representatives for in by the Fundamental Theorem of Galois Theory). This is a product of Galois conjugates of . In particular, if is Galois this is
(a) Prove that , so that the norm is a multiplicative map from to .
[This may be trivial, but I don't know how to show this.]