{
  "abstract": "Let $F$ be a field and let $L$ be a loop. We call $L$ just-infinite if it is infinite and every nontrivial normal subloop has finite index, and we call the possibly nonassociative loop algebra $F[L]$ just-infinite if it is infinite-dimensional and every nonzero two-sided ideal has finite codimension. We first prove that just-infiniteness of $F[L]$ always implies just-infiniteness of $L$. Next, using the Chein construction, we show for every infinite group $G$ that $M(G,2)$ is just-infinite if and only if $G$ is just-infinite, and that $F[M(G,2)]$ is just-infinite if and only if $F[G]$ is just-infinite. We extend the algebraic equivalence to the generalized Moufang doubles $M(G,*,g_0)$ whenever $G$ is infinite and nonabelian. Finally, we construct a single locally finite, residually finite, nonassociative Moufang loop $L$ for which $F[L]$ is residually finite-dimensional, locally finite-dimensional, and just-infinite over every field, and we explain why infinite nonassociative RA loops cannot be just-infinite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21016",
  "author_total": 1,
  "authors": [
    {
      "name": "Thales Fernando Vilamaior Paiva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9x5eqre97h4n6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21016",
  "fulltext_url": null,
  "id": "9x5eqre97h4n6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21016",
  "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.RA"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7213917846",
  "pdf_url": "https://arxiv.org/pdf/2609.21016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9x5eqre97h4n6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.21016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Just-Infinite Loops and Loop Algebras",
  "title_text": "Just-Infinite Loops and Loop Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/9x5eqre97h4n6",
  "venue": "arXiv",
  "versions": []
}