English

The differential rank of a differential-valued field

Commutative Algebra 2018-10-26 v3

Abstract

We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation on a field of generalized power series and use this method to show that any totally ordered set can be realized as the principal differential rank of a H-field.

Keywords

Cite

@article{arxiv.1707.09493,
  title  = {The differential rank of a differential-valued field},
  author = {Salma Kuhlmann and Gabriel Lehéricy},
  journal= {arXiv preprint arXiv:1707.09493},
  year   = {2018}
}