{
  "abstract": "In this paper we present a new result that exhibits in a non-recursive fashion a primary decomposition of any monomial ideal. Our result is derived from the classical quotient-sum recursive procedure for determining a primary decomposition of any proper ideal in a commutative Noetherian ring. We also show how our result can be used as an algorithm for producing a primary decomposition directly from the exponent vectors of the minimal generators of the ideal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25409",
  "author_total": 1,
  "authors": [
    {
      "name": "Jacob Miller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5r1jn5jqhffww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25409",
  "fulltext_url": null,
  "id": "5r1jn5jqhffww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25409",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214090778",
  "pdf_url": "https://arxiv.org/pdf/2609.25409",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5r1jn5jqhffww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25409",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25409"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Primary decompositions via exponent matrices",
  "title_text": "Primary decompositions via exponent matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/5r1jn5jqhffww",
  "venue": "arXiv",
  "versions": []
}