{
  "abstract": "We study the behavior of trace ideals under taking syzygies. In particular, when $R$ is numerical semigroup ring and $I$ is a homogeneous ideal in $R$, we obtain an upper estimate for $\\operatorname{tr}_R(Ω^1_R(I))$, and we show this estimate is sharp when $I$ is the conductor ideal $\\mathfrak{c}_R$ of $R$. Using this result, we characterize the numerical semigroup rings for which $\\operatorname{tr}_R(M) \\subseteq \\operatorname{tr}_R(Ω^1_R(M))$ holds for every finitely generated $R$-module $M$. In a similar vein, we characterize numerical semigroup rings for which $\\operatorname{tr}_R(Ω^1_R(\\mathfrak{c}_R))=\\mathfrak{c}_R$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00707",
  "author_total": 3,
  "authors": [
    {
      "name": "Haydee Lindo"
    },
    {
      "name": "Justin Lyle"
    },
    {
      "name": "Sarasij Maitra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dqkw9zcbnvx4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00707",
  "fulltext_url": null,
  "id": "1dqkw9zcbnvx4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00707",
  "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",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7206172824",
  "pdf_url": "https://arxiv.org/pdf/2609.00707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dqkw9zcbnvx4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.00707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Trace ideals of syzygies",
  "title_text": "Trace ideals of syzygies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/1dqkw9zcbnvx4",
  "venue": "arXiv",
  "versions": []
}