A general Hensel's lemma (Q1588404)

Hensel's lemma is equivalent to a statement on the lifting of roots of a polynomial in one variable from the residue field to the original valued field. The authors prove a very general form of this version of Hensel's lemma for several polynomials in several variables over a ``semi-valued'' ring. The proof uses Newton's method (in a simplified form) for finding roots of functions and is based on a fixed point theorem for spherically complete ultrametric spaces. Several applications of this general form of Hensel's lemma are given in more special situations.