Symmetry of Non-Archimedean Absolute Values

Abstract

This paper analyzes and describes the properties of the non-Archimedean absolute values on rational functions fields that are invariant to the permutation of variables. We will discover that these special non-Archimedean absolute values, that will be called symmetric, have interesting properties that do not hold for the symmetric Krull valuations in general, due to the powerful Hensel's lemma that may be applied on local fields.