{
  "abstract": "We prove the Hassanzadeh-Nasrollah Nejad-Simis conjecture: if $f\\in (x_1,\\ldots,x_n)^2\\subsetneq k[[x_1,\\ldots,x_n]]$ has an isolated critical point and $\\operatorname{char}k=0$, then its Euler conductor $J_f:f$ is not contained in the Tjurina ideal $(J_f,f)$. More generally, if $A=R/I$ is a nonzero Noetherian $k$-algebra and $a=[f]\\in A$ is nilpotent with $d_{A/k}a=0$, then $I:f\\nsubseteq(I,f)$. For a local ring $(R,\\mathfrak n)$ we obtain the stronger noncontainment $I:f\\nsubseteq(I,f)+\\mathfrak n(I:f)$. The proof reduces a hypothetical containment to a self-exact square-zero element and detects its differential by the trace of a regular representation over the dual numbers. Finally, an explicit five-variable isolated singularity satisfies $J_f:f\\subseteq\\overline{J_f}$, disproving the integral-closure strengthening proposed by Ma and Zuo.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09833",
  "author_total": 2,
  "authors": [
    {
      "name": "Yizhi Zhang"
    },
    {
      "name": "Huaiqing Zuo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0g5bn6zym488.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09833",
  "fulltext_url": null,
  "id": "f0g5bn6zym488",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09833",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7220917721",
  "pdf_url": "https://arxiv.org/pdf/2610.09833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0g5bn6zym488.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09833"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Hassanzadeh-Nasrollah Nejad-Simis Conjecture on Euler Conductors",
  "title_text": "The Hassanzadeh-Nasrollah Nejad-Simis Conjecture on Euler Conductors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/f0g5bn6zym488",
  "venue": "arXiv",
  "versions": []
}