Valuation methods in group rings and in skew fields, I

In this first in a series of two papers we construct a family of discrete valuations in group rings of residually torsion-free nilpotent groups and extend these valuations to the Malcev–Neumann power series skew fields of these group rings. We apply these valuations to the study of these skew fields. In the second paper we will use our results and methods to study free fields and the universal fields of fractions K((X)) of the Magnus power series ring.