Normal basis theorem
= Normal basis theorem
{title2=$L\cong K[G]$}
For a finite <Galois extension> $L/K$ with group $G$, there is $\theta\in L$ such that the elements $g(\theta)$ form a $K$-basis. Equivalently the additive $K[G]$-module $L$ is a regular representation. Over <p-adic fields>, its <p-adic lattices> are thus commensurable with regular lattices; this is useful in <Herbrand quotient> calculations after applying a <p-adic logarithm> to deep <principal units>.