{
  "abstract": "Let $K$ be a totally real number field. We prove that the totally positive algebraic integers $\\mathcal O_K^+$ of $K$, viewed as an abstract additive semigroup, uniquely determine $K$. We also describe all the additive relations by giving a presentation of $\\mathcal O_K^+$ in terms of indecomposables as generators and a certain concrete set of generating relations. In fact, we obtain this presentation in a more general class of discrete semigroups which we call semilattices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09346",
  "author_total": 2,
  "authors": [
    {
      "name": "Vitezslav Kala"
    },
    {
      "name": "Ritoprovo Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dejhj5j81yyc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09346",
  "fulltext_url": null,
  "id": "3dejhj5j81yyc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09346",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7212124692",
  "pdf_url": "https://arxiv.org/pdf/2609.09346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dejhj5j81yyc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The addition on totally positive integers uniquely determines the totally real number field",
  "title_text": "The addition on totally positive integers uniquely determines the totally real number field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/3dejhj5j81yyc",
  "venue": "arXiv",
  "versions": []
}