{
  "abstract": "We study differential polynomial rings $R[t;δ]$ over $Γ$-graded rings, where $Γ$ is an arbitrary group. We show that $R[t;δ]$ admits a $Γ$-grading compatible with that of $R$ if and only if $δ$ is a $γ$-derivation for some $γ\\in C_Γ(Γ_R)$, and that this grading is unique once $°(t)=γ$ is fixed; if $δ\\neq0$, then $γ$ is itself uniquely determined by $δ$. We characterize the resulting graded ring by a universal property. We prove a characteristic-free center criterion for gr-simplicity whenever $Z(R[t;δ])$ is a graded subring; in characteristic zero, gr-simplicity is equivalent to $δ$-gr-simplicity of $R$ and $γ$-outerness of $δ$, extending Jordan's simplicity criterion to the graded setting. We further show that $R[t;δ]$ is gr-prime if and only if $R$ is $δ$-gr-prime, and that gr-Noetherianity of $R$ passes to $R[t;δ]$, recovering a graded Hilbert basis theorem as a special case. When $Γ$ is abelian, gr-simplicity and gr-primality are shown to be invariants of homogeneous graded Morita equivalence, and every ring homogeneously graded equivalent to $R[t;δ]$ via a compatible idempotent is again a graded differential polynomial ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Math. Nachr. (2026)",
  "arxiv": "2606.23352",
  "author_total": 1,
  "authors": [
    {
      "name": "Yassine Ait Mohamed"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8yxz4vskmjtq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23352",
  "fulltext_url": null,
  "id": "8yxz4vskmjtq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23352",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.23352",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8yxz4vskmjtq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2606.23352",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23352"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Graded differential polynomial rings",
  "title_text": "Graded differential polynomial rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/8yxz4vskmjtq0",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1002/mana.70286",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}