Submission date: 29 July 2017

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.

Mathematics Subject Classification: 12H05, 12J10, 12J15, 13F25, 16W60

Keywords and phrases: Valuation, differential field, differential-valued field, H-field, asymptotic couple, generalized power series

Full text arXiv 1707.09493: pdf, ps.