{
  "abstract": "Analogous to quasi-Frobenius rings, dual rings, and Johns rings, the classes of $p$-quasi-Frobenius rings, $p$-dual rings, $p$-Johns rings are introduced and used to discuss and settle principal analogues of the Faith-Menal, Faith, and FGF conjectures. A chain symmetry theorem establishes that for quasi-injective semi-projective modules with semiprime endomorphism ring, endonoetherianity and endoartinianity are equivalent and force the endomorphism ring to be semisimple artinian. Within this unified setting, it is shown that (1) two-sided $p$-Johns rings are $p$-quasi-Frobenius, giving a principal Faith-Menal analogue, with a counterexample showing that the one-sided hypothesis is insufficient; (2) semiprimary principal right ideal rings that are right injective and right Kasch are $p$-quasi-Frobenius-this affirmatively answers a question of Faith (Q2) in the principal two-sided ideal ring case and settles the principal Faith conjecture, with a counterexample showing the principal right ideal ring to be indispensable; and (3) right $p$-Johns rings that are left CF and left perfect are $p$-quasi-Frobenius, yielding a principal FGF analogue, with a counterexample demonstrating that the hypotheses are essential. Wherever needed, examples are provided to show that various classes introduced are different from the existing classes in the literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18492",
  "author_total": 4,
  "authors": [
    {
      "name": "Theophilus Gera"
    },
    {
      "name": "Amit Sharma"
    },
    {
      "name": "Manoj Kumar Patel"
    },
    {
      "name": "Pramod Kanwar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74d8724ef3bcp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18492",
  "fulltext_url": null,
  "id": "74d8724ef3bcp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18492",
  "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": "W7221818385",
  "pdf_url": "https://arxiv.org/pdf/2610.18492",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74d8724ef3bcp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.18492",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18492"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Endochain conditions on modules and $p$-quasi-Frobenius rings",
  "title_text": "Endochain conditions on modules and p-quasi-Frobenius rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/74d8724ef3bcp",
  "venue": "arXiv",
  "versions": []
}