{
  "abstract": "We study automorphic transcendence degree for quotients of multivariate skew polynomial rings over a division ring D. We identify this invariant with relative growth dimension, the degree of the relative Hilbert polynomial, and a coordinate dimension determined by leading monomials. We establish invariance under finite module extensions, integral extensions, and investigate the Gelfand-Kirillov dimension under a local finiteness condition. When the coefficient automorphisms are independent modulo inner automorphisms, we prove that a quotient is automorphically normalizable precisely when its automorphic transcendence degree equals the number of nonnilpotent coordinate variables, and classify all such normalization subrings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23713",
  "author_total": 3,
  "authors": [
    {
      "name": "Dinh Van Hoang"
    },
    {
      "name": "Vo Ngoc Thieu"
    },
    {
      "name": "Phan Thanh Toan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0dkzwq7aakt8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23713",
  "fulltext_url": null,
  "id": "c0dkzwq7aakt8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23713",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7214046905",
  "pdf_url": "https://arxiv.org/pdf/2609.23713",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0dkzwq7aakt8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23713",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23713"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Automorphic Transcendence Degree, Growth, and Skew Normalization",
  "title_text": "Automorphic Transcendence Degree, Growth, and Skew Normalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/c0dkzwq7aakt8",
  "venue": "arXiv",
  "versions": []
}