{
  "abstract": "We study integral dependence over left ideals using G-left ideals, namely left ideals maximal with respect to the failure of integrality of a fixed element. We establish several characterizations of G-left ideals, and show that their intersection is precisely the upper nilradical. Motivated by the Köthe conjecture, we introduce the class of left KI-rings as rings in which sums of left ideals integral over a fixed left ideal remain integral over that ideal. It is shown that left artinian rings, PI-rings, algebraic algebras, and algebras of dimension smaller than the cardinality of the ground field are left KI-rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26909",
  "author_total": 1,
  "authors": [
    {
      "name": "Masood Aryapoor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n67kfqbrsa16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26909",
  "fulltext_url": null,
  "id": "7n67kfqbrsa16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26909",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7214229243",
  "pdf_url": "https://arxiv.org/pdf/2609.26909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7n67kfqbrsa16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Integral Dependence over One-Sided Ideals, Part II: G-Left Ideals and the Köthe Problem",
  "title_text": "Integral Dependence over One-Sided Ideals, Part II: G-Left Ideals and the Köthe Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/7n67kfqbrsa16",
  "venue": "arXiv",
  "versions": []
}