{
  "abstract": "Let $I$ be a monomial ideal in $S=\\mathbb{k}[x_1,\\ldots,x_n]$, and set $R=S/I$. We prove that if $I$ is $\\mathbf{a}$-bounded and $M$ is a positively $\\mathbf{b}$-determined $R$-module, then $\\mathrm{tr}_R(M)$ is $(\\mathbf{a}+\\mathbf{b})$-bounded. For the canonical module, this gives the bound $2\\mathbf{a}$. In particular, the canonical trace ideal of every Stanley--Reisner ring is a cube-free monomial ideal. We also prove that, for a Stanley--Reisner ring satisfying $(S_2)$, the canonical trace ideal is the square of its radical if and only if the ring satisfies $(G_2)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00714",
  "author_total": 1,
  "authors": [
    {
      "name": "Sora Miyashita"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ez1zcjqj2wtd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00714",
  "fulltext_url": null,
  "id": "8ez1zcjqj2wtd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00714",
  "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/2611.00714",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ez1zcjqj2wtd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00714",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00714"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings",
  "title_text": "Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8ez1zcjqj2wtd",
  "venue": "arXiv",
  "versions": []
}