Strong and Explicit Forms of the One-Sided Nullstellensatz over Division Rings

Masood Aryapoor

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arXiv · 2609.34278

Strong and Explicit Forms of the One-Sided Nullstellensatz over Division Rings

Masood Aryapoor

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Abstract

We establish strong and explicit forms of a one-sided Nullstellensatz for polynomial rings D[x1, . . . , xn] over arbitrary division rings D with central indeterminates. To this end, we employ the theory of integral dependence over left ideals and the notion of G-left ideals, which plays a role analogous to that of G-ideals in the classical theory. We prove that the Jacobson radical of any left ideal of D[x1, . . . , xn] coincides with the intersection of all G-left ideals containing it. As a consequence, we obtain an explicit description of Jacobson radicals of left ideals of polynomial rings over division rings in terms of integral dependence.

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BibTeX RIS

Masood Aryapoor. 2026-09-28. Strong and Explicit Forms of the One-Sided Nullstellensatz over Division Rings. https://arxiv.org/abs/2609.34278

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