The differential rank of a differential-valued field

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.

References in corpus (2)

• The valuation difference rank of a quasi-ordered difference field
• A Baer-Krull theorem for quasi-ordered groups

Cited by in corpus (1)

• A structure theorem for abelian quasi-ordered groups