{
  "abstract": "Let $φ\\colon A\\to B$ be a Jordan homomorphism of associative algebras over a field $\\mathbb{F}$ of characteristic different from $2$, with defect ideals $V_φ$ and $W_φ$. If $A=\\operatorname{Alg}([[A,A],[A,A]])$, then $V_φW_φ=W_φV_φ=0$ and $V_φ\\cap W_φ\\subseteq\\operatorname{Ann}(\\operatorname{Alg}(φ(A)))$. Moreover, the induced map modulo $V_φ\\cap W_φ$ is standard. The annihilator bound is sharp, even in finite dimension. As an application, when $A$ is unital and $A=K(A)$, every Jordan homomorphism defined on $A$ is splittable and standard. In this setting, the corresponding result of Brešar and Zelmanov holds without the surjectivity hypothesis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17518",
  "author_total": 1,
  "authors": [
    {
      "name": "Cao Minh Nam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cq1zfmm5q0n9w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17518",
  "fulltext_url": null,
  "id": "cq1zfmm5q0n9w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17518",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221814526",
  "pdf_url": "https://arxiv.org/pdf/2610.17518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cq1zfmm5q0n9w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Orthogonality of Defect Ideals for Jordan Homomorphisms",
  "title_text": "Orthogonality of Defect Ideals for Jordan Homomorphisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/cq1zfmm5q0n9w",
  "venue": "arXiv",
  "versions": []
}