\begin{definition}[Definition:Field Norm/Definition 2]
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 $\map {\operatorname{Gal}} {L / K}$ is finite.
The '''field norm''' $\map {N_{L / K}} \alpha$ of $\alpha$ is $\ds \prod_{\sigma \mathop \in \map {\operatorname{Gal}} {L / K}} \map \sigma \alpha$.
\end{definition}