I am in trouble with reading Neukirch, Algebraic-Number-Theory, Chap.II.4.6(Hensel's lemma).
Question: Do we need the assumption of discreteness for nonarchimedian valuations in Hensel's Lemma(4.6) and Theorem (4.8)(Extension of valuation)?
In II.4.6(page 129), the statement does not include discreteness but it uses discreteness in its proof, page 130,line 10. (It uses 4.5, which deals with discrete valuations.) If we have to add the assumption of discreteness, we have to add the same for 4.7 and 4.8 because of their proofs. But inserting discreteness into 4.8 looks strange.