{
  "abstract": "We prove an analogue of Hilbert's basis theorem for Poisson Ore extensions and Poisson Laurent Ore extensions. We also obtain corresponding results for iterated Poisson Ore extensions and iterated Poisson Laurent Ore extensions associated to commuting Poisson-pairs. Finally, we give examples of Poisson Ore extensions that are Poisson-Noetherian without being Noetherian as ordinary algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Math. Nachr. (2026)",
  "arxiv": "2606.14660",
  "author_total": 4,
  "authors": [
    {
      "name": "Per Bäck"
    },
    {
      "name": "Patrik Lundström"
    },
    {
      "name": "Johan Öinert"
    },
    {
      "name": "Johan Richter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cy2bm4a8hfdy0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.14660",
  "fulltext_url": null,
  "id": "cy2bm4a8hfdy0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.14660",
  "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.AC"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.14660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cy2bm4a8hfdy0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2606.14660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.14660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hilbert's basis theorem for Poisson Ore extensions",
  "title_text": "Hilbert's basis theorem for Poisson Ore extensions",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/cy2bm4a8hfdy0",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1002/mana.70248",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}