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}
}