On the non-uniqueness of maximal purely wild extensions

TL;DR

This paper explores conditions under which henselian valued fields can have multiple non-isomorphic maximal purely wild extensions, highlighting the non-uniqueness phenomenon in valuation theory.

Contribution

It provides criteria that guarantee the existence of non-unique maximal purely wild extensions for henselian valued fields.

Findings

Criteria for non-uniqueness of maximal purely wild extensions

Examples illustrating non-isomorphic extensions

Conditions under which uniqueness fails

Abstract

In this paper we illustrate certain criteria which are sufficient for a henselian valued field to admit non-isomorphic maximal purely wild extensions.