A generalization of Hensel's lemma (Q1281117)

The ``generalization of Hensel's lemma'' referred to in the title is a sufficient condition for a polynomial \(f\in F[x]\) to be reducible, where \(F\) is a Henselian valued field. The novel feature, compared with the usual Hensel's lemma, is that the coefficients of the polynomial in question are not required to belong to the valuation ring. The proof uses the associated graded field of a valued field. The paper contains an unusually large number of bad misprints. At some points it is even difficult to understand the intended meaning. The author is not always careful about stating the hypotheses of his results.