{
  "abstract": "We study Bass's finiteness problem for embeddings into proper quotients. Given a commutative ring R, a reduced finitely generated R-algebra A, and an ideal $J\\triangleleft A$, we ask whether an R-algebra monomorphism $A\\hookrightarrow_R A/J$ forces J=0. We give affirmative answers by presenting two arguments. Also, we discuss not only in the reduced case, but also in several non-reduced cases: when R is artinian and A is finite over R; when R is zero-dimensional and A is finite projective over R; and in a series of Cohen--Macaulay settings. In the module-theoretic direction, for a noetherian reduced ring, and a finitely generated, and torsion-free A-module M, we show that $M\\hookrightarrow_R M/JM$ implies that J is contained in a minimal prime of A; if M is faithful, then J=0. Also, dual versions investigated. Examples illustrate the necessity of hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25845",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohsen Asgharzadeh"
    },
    {
      "name": "Elham Mahdavi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkmz39g7jtvvz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25845",
  "fulltext_url": null,
  "id": "bkmz39g7jtvvz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25845",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7223065677",
  "pdf_url": "https://arxiv.org/pdf/2610.25845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkmz39g7jtvvz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25845"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Embedding into quotient",
  "title_text": "Embedding into quotient",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/bkmz39g7jtvvz",
  "venue": "arXiv",
  "versions": []
}