N. Regnault

collaborators

3 papers

math.LO2020

Differential exponential topological fields

Francoise Point, Nathalie Regnault

We axiomatize a class of existentially closed exponential fields equipped with an $E$ -derivation. We apply our results to the field of real numbers endowed with $e x p (x)$ the classi…

math.AC2020

Exponential ideals and a Nullstellensatz

Francoise Point, Nathalie Regnault

We prove a version of a Nullstellensatz for partial exponential fields $(K, E)$ , even though the ring of exponential polynomials $K [X_{1}, \dots, X_{n}]^{E}$ is not a Hilbert ring. We show…

math.LO2020

Coincidence of dimensions in closed ordered differential fields

Pantelis E. Eleftheriou, Omar Leon Sanchez, Nathalie Regnault

Let $K = ⟨ R, δ ⟩$ be a closed ordered differential field, in the sense of M. Singer, and $C$ its field of constants. In this note, we prove that, for set…