3 papers
math.RA2025
A quantitative Hilbert's basis theorem and the constructive Krull dimension
Ryota Kuroki
In classical mathematics, Gulliksen has introduced the length of Noetherian modules, and Brookfield has determined the length of Noetherian polynomial rings. Brookfield's result ca…
math.AC2025
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…
math.AC2025
A quantitative general Nullstellensatz for Jacobson rings
Ryota Kuroki
The general Nullstellensatz states that if is a Jacobson ring, is Jacobson. We introduce the notion of an -Jacobson ring for an ordinal and prove a quantitative…