{
  "abstract": "For a finite ring $R$, we investigate the probability that the product of two randomly chosen elements in $R$ is nilpotent, which we call the nilpotent product probability (NPP) of $R$ and denote by $P_{nil}(R)$. We derive bounds for $P_{nil}(R)$ that depend on the structure of $R$, and prove that among all commutative rings with identity, the class of local rings with residue field $\\mathbb{Z}_{2}$ attains the maximum value of NPP, which is equal to $3/4$. Further, we determine the set of all values of NPP for commutative rings with identity and classify all rings attaining those values. Finally, we investigate the relationship between NPP of $R$ and NPP of some subrings of the matrix ring over $R$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07892",
  "author_total": 2,
  "authors": [
    {
      "name": "Dibyasman Sarma"
    },
    {
      "name": "Tikaram Subedi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/274d1n0mj90qx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07892",
  "fulltext_url": null,
  "id": "274d1n0mj90qx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07892",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7221030201",
  "pdf_url": "https://arxiv.org/pdf/2610.07892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/274d1n0mj90qx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nilpotent Product Probability of Finite Rings",
  "title_text": "Nilpotent Product Probability of Finite Rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/274d1n0mj90qx",
  "venue": "arXiv",
  "versions": []
}