{
  "abstract": "We study Poisson algebras in which every Poisson subalgebra is a Poisson ideal, called Dedekind Poisson algebras, over arbitrary fields and without any finite-dimensionality assumption. In characteristic different from 2, combining the two operations by $x*y=xy+[x,y]$ connects the problem with Outcalt's classical classification of power-associative H-algebras and yields the same structural type. We obtain a complete classification by a direct two-operation argument valid in every characteristic. This approach also shows that characteristic 2 retains additional Poisson information which cannot be recovered from the single product $*$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13767",
  "author_total": 2,
  "authors": [
    {
      "name": "A. I. Plakosh"
    },
    {
      "name": "O. O. Pypka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fp4dbfrwzyq66.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13767",
  "fulltext_url": null,
  "id": "fp4dbfrwzyq66",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13767",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213254900",
  "pdf_url": "https://arxiv.org/pdf/2609.13767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fp4dbfrwzyq66.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Dedekind Poisson Algebras over Arbitrary Fields",
  "title_text": "Dedekind Poisson Algebras over Arbitrary Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fp4dbfrwzyq66",
  "venue": "arXiv",
  "versions": []
}