 Cyclic local norm index (source code)

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= Cyclic local norm index
{title2=$[K^\times:N_{L/K}L^\times]=[L:K]$}

For a cyclic extension of <p-adic fields>, the <Herbrand quotient of the local multiplicative group> together with <Hilbert theorem 90> gives this index. If the ramification index and residue degree are $e,f$, the norm valuation formula $v_K(Nx)=f v_L(x)$ then gives the unit norm index $e$. In particular all units are norms in an <unramified extension>.

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