On generalized series fields and exponential-logarithmic series fields with derivations

TL;DR

This paper surveys properties of generalized series and exponential-logarithmic series fields, focusing on their differential structures, based on collaborative research, to understand their algebraic and differential properties.

Contribution

It provides a comprehensive overview of the differential structures of these series fields, highlighting new insights from recent joint work.

Findings

Characterization of differential structures on series fields

Identification of key properties of exponential-logarithmic series

Connections between algebraic and differential aspects of the fields

Abstract

We survey some important properties of fields of generalized series and of exponential-logarithmic series, with particular emphasis on their possible differential structure, based on a joint work of the author with S. Kuhlmann [KM12b,KM11].