  Let R be a complete discrete valuation ring with maximal ideal generated by
pi. Let f(X) in R[X] be a monic polynomial with nonzero discriminant Delta(f).
Let s >= v_pi(Delta(f)) + 1. Suppose given a factorisation of f(X) in (R/pi^s
R)[X] into several factors, not necessarily coprime in (R/pi R)[X]. We lift it
uniquely to a factorisation of f(X) in R[X]. This generalises the
Hensel-Rychlik Lemma, which covers the case of two factors. We work directly
with lifts of factorisations into several factors and avoid having to iterate
factorisations into two factors. For this purpose we define a resultant for
several polynomials in one variable as determinant of a generalised Sylvester
matrix.

Commutative Algebra