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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	339-352
Number of pages	13
Journal	ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik
Volume	72
DOIs	https://doi.org/10.60866/CAM.292
Publication status	Published - 20 Jan 2026

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10.60866/CAM.292

Cite this

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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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AU - Point, Francoise

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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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DO - 10.60866/CAM.292

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