Remark 1

Let F be an extension of K and $N$ a subextension of F, and let $\Gamma$ be a finite group of automorphisms of $N$, of which K is the field of invariants. Prop. 8 implies the existence of an isomorphism of K-algebras $0 : N \otimes_F F \to F^\Gamma$ characterized by $\theta(x \otimes y)\,(a) = \sigma(x)\,y$ for $x \in N,\,y \in F$ and $\sigma \in \Gamma$.