{
  "abstract": "We construct a class of positive cones that make $\\C$ into a directed partially ordered ring. The positive cones are defined using integral closures of local rings, associated with a transcendence basis and a chosen real generator. A localization criterion also yields such orders on every transcendental extension of $\\Q$. For a fixed coefficient field, we prove that two real generators define the same cone if and only if they differ by an affine map with positive real-algebraic slope and translation algebraic over that field. The nonzero positive elements are closed under inversion. None of these orders is a lattice order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20494",
  "author_total": 4,
  "authors": [
    {
      "name": "Wenyi Wang"
    },
    {
      "name": "Ruisong Yuan"
    },
    {
      "name": "Yuehui Zhang"
    },
    {
      "name": "Yuhang Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1adx5f9sx7xws.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20494",
  "fulltext_url": null,
  "id": "1adx5f9sx7xws",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20494",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7213579190",
  "pdf_url": "https://arxiv.org/pdf/2609.20494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1adx5f9sx7xws.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Directed partial orders on the complex number field",
  "title_text": "Directed partial orders on the complex number field",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:43Z",
  "url": "https://research.draconitic.com/paper/1adx5f9sx7xws",
  "venue": "arXiv",
  "versions": []
}