{
  "abstract": "Let $I$ be a non-nilpotent graded ideal of a standard graded algebra over a Noetherian commutative ring. We show that the saturation degree sdeg $I^n$ is asymptotically a constant function or a linear function whose slope is one of the generating degrees of $I$. Furthermore, we give sufficient (and necessary) conditions for a numerical functions to be the function sdeg $I^n$ of an ideal $I$ generated by forms of the same degree. Our results may provide a better understanding of the initial behavior of the regularity function reg $I^n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Journal of Pure and Applied Algebra 230 (2026), Issue 10, JPAA_108392",
  "arxiv": "2610.26532",
  "author_total": 3,
  "authors": [
    {
      "name": "Le Tuan Hoa"
    },
    {
      "name": "Hop Dang Nguyen"
    },
    {
      "name": "Ngo Viet Trung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dc4q7a948v7xg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26532",
  "fulltext_url": null,
  "id": "dc4q7a948v7xg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26532",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.26532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dc4q7a948v7xg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Saturation degree of powers of graded ideals",
  "title_text": "Saturation degree of powers of graded ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dc4q7a948v7xg",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.jpaa.2026.108392",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}