Eisenstein generator of a totally ramified extension
= Eisenstein generator of a totally ramified extension
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A finite extension $L/K$ of complete discretely valued fields is totally ramified exactly when $L=K(\alpha)$ for a root $\alpha$ of an <Eisenstein polynomial> over $\mathcal O_K$. In the reverse direction one may take $\alpha$ to be any <uniformizer> of $L$.