{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34278",
  "author_total": 1,
  "authors": [
    {
      "name": "Masood Aryapoor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f63f0c51ykas7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34278",
  "fulltext_url": null,
  "id": "f63f0c51ykas7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34278",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7214798403",
  "pdf_url": "https://arxiv.org/pdf/2609.34278",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f63f0c51ykas7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34278",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34278"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Strong and Explicit Forms of the One-Sided Nullstellensatz over Division Rings",
  "title_text": "Strong and Explicit Forms of the One-Sided Nullstellensatz over Division Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/f63f0c51ykas7",
  "venue": "arXiv",
  "versions": []
}