Exponential ideals and a Nullstellensatz

Nathalie Regnault; Francoise Point

doi:10.60866/CAM.292

Exponential ideals and a Nullstellensatz

Nathalie Regnault
, Francoise Point

Applied Crypto Expertise

Université Paris-Cité

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We prove a version of a Nullstellensatz for partial exponential fields (F,E) , even though the ring of exponential polynomials F[X]^E is not a Hilbert ring. We show that under certain natural conditions, one can embed an ideal of F[X]^E into an exponential ideal. In case the ideal consists of exponential polynomials with one iteration of the exponential function, we show that these conditions can be met. We apply our results to the case of ordered exponential fields.

langue originale	Anglais
Pages (de - à)	339-352
Nombre de pages	13
journal	ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik
Volume	72
Les DOIs	https://doi.org/10.60866/CAM.292
état	Publié - 20 janv. 2026

mots-clés

Model Theory, Exponential Algebra, Exponential Polynomials

Accès au document

10.60866/CAM.292

Contient cette citation

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title = "Exponential ideals and a Nullstellensatz",

abstract = "We prove a version of a Nullstellensatz for partial exponential fields (F,E) , even though the ring of exponential polynomials F[X]\textasciicircum{}E is not a Hilbert ring. We show that under certain natural conditions, one can embed an ideal of F[X]\textasciicircum{}E into an exponential ideal. In case the ideal consists of exponential polynomials with one iteration of the exponential function, we show that these conditions can be met. We apply our results to the case of ordered exponential fields.",

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AB - We prove a version of a Nullstellensatz for partial exponential fields (F,E) , even though the ring of exponential polynomials F[X]^E is not a Hilbert ring. We show that under certain natural conditions, one can embed an ideal of F[X]^E into an exponential ideal. In case the ideal consists of exponential polynomials with one iteration of the exponential function, we show that these conditions can be met. We apply our results to the case of ordered exponential fields.

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