Valuation Leveling on Rational Function Fields

Abstract

Since a new field of research in the theory of valuations has been opened by the notion of symmetric extensions of a valuation on a field K to K(X1,…, Xn), with respect to the indeterminates X1,…, Xn, it makes sense to look for applications of this theory in dealing with arbitrary valuations on rational function fields. This paper investigates the conditions and methods of transforming asymmetric valuations on rational function fields into symmetric ones - procedure that will be called valuation leveling - the motivation being the opportunity of applying the specific results from the theory of symmetric valuations in the general case.