Ryota Kuroki

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math.AC2025

A quantitative general Nullstellensatz for Jacobson rings

Ryota Kuroki

The general Nullstellensatz states that if $A$ is a Jacobson ring, $A [X]$ is Jacobson. We introduce the notion of an $α$ -Jacobson ring for an ordinal $α$ and prove a quantitative v…

math.AC2024

A constructive proof of the general Nullstellensatz for Jacobson rings

Ryota Kuroki

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 gen…