p-adic field
= p-adic field
{title2=$[K:\mathbb Q_p]<\infty$}
A p-adic field is a finite extension of the <P-adic number> field $\mathbb Q_p$, equipped with its extended <p-adic absolute value>. Conversely every characteristic-zero, nontrivially valued, non-Archimedean locally compact field is such an extension. A finite quotient $\mathcal O/p\mathcal O$ supplies finitely many generators of $\mathcal O$ over $\mathbb Z_p$ by repeated reduction and completeness.