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arXiv · 2406.06078

A constructive proof of the general Nullstellensatz for Jacobson rings

Ryota Kuroki
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Abstract

We give a constructive proof of the general Nullstellensatz: a univariate polynomial ring over a commutative Jacobson ring is Jacobson. This theorem implies that every finitely generated algebra over a zero-dimensional ring or the ring of integers is Jacobson, which has been an open problem in constructive algebra. We also prove a variant of the general Nullstellensatz for finitely Jacobson rings.

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Ryota Kuroki. 2024-06-10. A constructive proof of the general Nullstellensatz for Jacobson rings. https://doi.org/10.1080/00927872.2025.2554952

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