{
  "abstract": "We introduce and study sdf-absorbing factorization rings (SAF-rings), in which every regular ideal is a finite product of square-difference factor absorbing ideals. We investigate their behavior under direct products, localizations, factor rings, and module idealizations, and establish connections with SP-rings, Dedekind rings, and N-rings. We also introduce strongly sdf-absorbing factorization rings (SSAF-rings), relate them to SSP-rings and almost multiplication rings, and prove that the Noetherian SSAF-rings are precisely the ZPI-rings. Applications to module idealizations and monoid rings are also presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20884",
  "author_total": 4,
  "authors": [
    {
      "name": "Malik Tusif Ahmed"
    },
    {
      "name": "Hwankoo Kim"
    },
    {
      "name": "Hafnaoui Hidouri"
    },
    {
      "name": "Ahmed Hamed"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2d9twhfhv7af2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20884",
  "fulltext_url": null,
  "id": "2d9twhfhv7af2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20884",
  "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|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7222669559",
  "pdf_url": "https://arxiv.org/pdf/2610.20884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2d9twhfhv7af2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.20884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Commutative rings with square-difference factor absorbing factorization",
  "title_text": "Commutative rings with square-difference factor absorbing factorization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/2d9twhfhv7af2",
  "venue": "arXiv",
  "versions": []
}