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 $\Gal \left({L / K}\right)$ is finite.

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