{
  "abstract": "In this paper, we give conditions on a unital non-associative ring $R$ and additive map $σ: R\\longrightarrow R$ so that the non-associative skew power series ring, denoted by $R[[X;σ]]$ and the non-associative skew Laurent series ring denoted by $R((X;σ))$ are left (resp. right) Noetherian, respectively. Consequently, we establish versions of Hilbert Basis Theorem of $R[[X;σ]]$ and $R((X;σ))$, respectively, for left (resp. right) Noetherianity . We also give a counterexample showing that the Hilbert Basis Theorem does not hold in general in the non-associative case. In establishing the Hilbert Basis Theorems for $R[[X;σ]]$ and $R((X;σ))$, we introduce and utilize the right (resp. left) quasi-associative property of $R$, which is equivalent to $rR$ (resp. $Rc$) being one-sided ideals for all $r\\in R$ (resp. $c\\in R$).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31486",
  "author_total": 3,
  "authors": [
    {
      "name": "Darwin P. Mangubat"
    },
    {
      "name": "Jocelyn P. Vilela"
    },
    {
      "name": "Johan Richter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1v243a66yqj6r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31486",
  "fulltext_url": null,
  "id": "1v243a66yqj6r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31486",
  "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": "W7214650947",
  "pdf_url": "https://arxiv.org/pdf/2609.31486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1v243a66yqj6r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Hilbert Basis Theorem for Non-Associative Skew Power Series Rings and Non-Associative Skew Laurent Series Rings over a Non-Associative Coefficient Ring",
  "title_text": "The Hilbert Basis Theorem for Non-Associative Skew Power Series Rings and Non-Associative Skew Laurent Series Rings over a Non-Associative Coefficient Ring",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/1v243a66yqj6r",
  "venue": "arXiv",
  "versions": []
}