{
  "abstract": "We undertake a systematic study of multiplicative monoid morphisms between prime-power modular monoids $(\\mathbb{Z}/p^e\\mathbb{Z},\\cdot)$ and $(\\mathbb{Z}/q^f\\mathbb{Z},\\cdot)$, for arbitrary primes $p,q$ and integers $e,f\\geq 1$. Our approach proceeds in three stages. We first determine the hom-set $\\mathbf{Hom}(U_{p^e},U_{q^f})$ of group morphisms between the corresponding unit groups and exhibit explicit isomorphisms describing its group structure. We then identify the subset $\\mathcal{H}_{p^e,q^f,v}$ of unit group morphisms that extend to full monoid morphisms on $(\\mathbb{Z}/p^e\\mathbb{Z},\\cdot)$, characterizing it via explicit divisibility conditions and describing its algebraic structure. Finally, we give a complete description of $\\mathbf{Hom}_{\\mathbf{Mon}}((\\mathbb{Z}/p^e\\mathbb{Z},\\cdot), (\\mathbb{Z}/q^f\\mathbb{Z},\\cdot))$ and establish an explicit monoid isomorphism between this hom-set and a naturally defined monoid built from unit groups of lower-level modular rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02393",
  "author_total": 3,
  "authors": [
    {
      "name": "Joseph Atalaye"
    },
    {
      "name": "Liam Baker"
    },
    {
      "name": "Sophie Marques"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xdr9jb8jjgcd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02393",
  "fulltext_url": null,
  "id": "7xdr9jb8jjgcd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02393",
  "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": "W7220445516",
  "pdf_url": "https://arxiv.org/pdf/2610.02393",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xdr9jb8jjgcd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02393",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02393"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Prime-Power Multiplicative Modular Monoid Morphisms",
  "title_text": "Prime-Power Multiplicative Modular Monoid Morphisms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/7xdr9jb8jjgcd",
  "venue": "arXiv",
  "versions": []
}