= Norm of an integral element over a normal domain
{title2=$N_{L/K}(b)\in A$}
Let $A$ be an <integrally closed domain> with fraction field $K$, and let $L/K$ be finite. If $b\in L$ is an <integral element> over $A$, its monic <minimal polynomial> lies in $A[T]$: its roots are integral, so its coefficients are integral elements of $K$, hence belong to $A$. If that polynomial has degree $r$ and constant coefficient $a_0$, then $N_{L/K}(b)=((-1)^ra_0)^{[L:K(b)]}\in A$. This remains true for inseparable extensions. An infinite algebraic extension has no usual determinant field norm.
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