Valued modules over skew polynomial rings 1

TL;DR

This paper develops a theory of valued modules tailored for positive characteristic valued fields, establishing a framework for henselianity and proving Ax-Kochen Ershov type theorems.

Contribution

It introduces the concept of valued modules for positive characteristic fields and constructs a henselianity theory within this framework, extending existing valuation theories.

Findings

Established a notion of valued modules suitable for positive characteristic fields.

Developed a henselianity theory in the language of valued modules.

Proved Ax-Kochen Ershov type results for these structures.

Abstract

We introduce a notion of valued module which is suitable to study valued fields of positive characteristic. Then we built-up a robust theory of henselianity in the language of valued modules and prove Ax-Kochen Ershov type results.