{
  "abstract": "Determining whether an algebraic number field admits a power integral basis is a classical problem, but it can be difficult for fields defined by polynomial compositions and dynamical iterates. In this paper, we study the monogeneity of compositions $f(h(x))$, where $f(x)$ and $h(x)$ are monic polynomials over an arbitrary Krull valuation ring and $h(x)$ is a trinomial. We derive explicit formulas for the discriminant of the composition and use them to characterize when $f(h(x))$ generates a monogenic field. In particular, we relate the monogeneity of the composition to that of $f(x)$ and to explicit square-free conditions on the critical values of $h(x)$. We further extend the results to polynomial iteration and obtain a criterion for the monogeneity of binomial iterates, yielding new infinite families of monogenic fields. Finally, we give quantitative results and illustrate our criteria with several examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02111",
  "author_total": 4,
  "authors": [
    {
      "name": "Anuj Jakhar"
    },
    {
      "name": "Ravi Kalwaniya"
    },
    {
      "name": "Shanta Laishram"
    },
    {
      "name": "Prabhakar Yadav"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9wck0zwdt4e3y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02111",
  "fulltext_url": null,
  "id": "9wck0zwdt4e3y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02111",
  "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.NT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7216316409",
  "pdf_url": "https://arxiv.org/pdf/2610.02111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9wck0zwdt4e3y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02111"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On The Index of Polynomial Compositions over Valued Fields",
  "title_text": "On The Index of Polynomial Compositions over Valued Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/9wck0zwdt4e3y",
  "venue": "arXiv",
  "versions": []
}