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arXiv · 1707.09493

The differential rank of a differential-valued field

Salma Kuhlmann·Gabriel Lehéricy
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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.

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Salma Kuhlmann, Gabriel Lehéricy. 2018-06-27. The differential rank of a differential-valued field. https://doi.org/10.1007/s00209-018-2132-z

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