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

Onderzoeksoutput: Bijdrage aan een tijdschrift › Artikel › peer review

Samenvatting

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.

Originele taal-2	Engels
Pagina's (van-tot)	339-352
Aantal pagina's	13
Tijdschrift	ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik
Volume	72
DOI's	https://doi.org/10.60866/CAM.292
Status	Gepubliceerd - 20 jan 2026

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10.60866/CAM.292

Citeer dit

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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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