{
  "id": "2505.09635",
  "version": "v1",
  "published": "2025-05-04T11:00:36.000Z",
  "updated": "2025-05-04T11:00:36.000Z",
  "title": "On ideal class groups of totally degenerate number rings",
  "authors": [
    "Ruben Hambardzumyan",
    "Mihran Papikian"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\chi(x)\\in \\mathbb{Z}[x]$ be a monic polynomial whose roots are distinct integers. We study the ideal class monoid and the ideal class group of the ring $\\mathbb{Z}[x]/(\\chi(x))$. We obtain formulas for the orders of these objects, and study their asymptotic behavior as the discriminant of $\\chi(x)$ tends to infinity, in analogy with the Brauer-Siegel theorem. Finally, we describe the structure of the ideal class group when the degree of $\\chi(x)$ is $2$ or $3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-04T11:00:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R54",
      "15B36"
    ],
    "keywords": [
      "ideal class group",
      "totally degenerate number rings",
      "ideal class monoid",
      "distinct integers",
      "monic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}