{
  "abstract": "Let $A_\\bullet$ and $B_\\bullet$ be nonnegatively graded algebras, finitely generated in degrees less than $2$ and with semisimple base rings $A_0$ and $B_0$. We prove that if $A \\simeq B$ as ungraded algebras, then $A_\\bullet \\simeq B_\\bullet$ as graded algebras. This generalises a theorem of Bell and Zhang arXiv:1509.08812 in the connected case $A_0 = k = B_0$, and the path-algebra version when $A_0$ and $B_0$ are $k$-elementary due to Gaddis arXiv:1712.01650. We also discuss some related open problems for graded algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03288",
  "author_total": 1,
  "authors": [
    {
      "name": "Darius Dramburg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/434g7efcracyr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03288",
  "fulltext_url": null,
  "id": "434g7efcracyr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03288",
  "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|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7208756913",
  "pdf_url": "https://arxiv.org/pdf/2609.03288",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/434g7efcracyr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03288",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03288"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Isomorphisms of graded semiconnected algebras",
  "title_text": "Isomorphisms of graded semiconnected algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/434g7efcracyr",
  "venue": "arXiv",
  "versions": []
}