Definition:Field Norm/Definition 2

Definition
Let $K$ be a field and $L / K$ a finite field extension of $K$.

Let $\alpha\in L$. Let $L/K$ be Galois.

By Finite Field Extension has Finite Galois Group, the Galois group $\Gal(L/K)$ is finite.

The field norm $N_{L/K} \left({\alpha}\right)$ of $\alpha$ is $\displaystyle\prod_{\sigma\in\operatorname{Gal}(L/K)}\sigma(\alpha)$.