On a $q$-Skew Amitsur's Theorem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913104083812352 |
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| author | Launois, Aristide F. J. -C. |
| author_facet | Launois, Aristide F. J. -C. |
| contents | Let $R$ be an algebra over an uncountable field, $σ$ a locally torsion automorphism and $δ$ a locally nilpotent left $σ$-derivation such that $qσδ= δσ$, where $q$ is a nonzero scalar. We show that the constant part of the Jacobson radical of the Ore extension $R[x;σ,δ]$ is nil. This partially answers a question of Greenfeld, Smoktunowicz and Ziembowski posed in 2019. As a corollary, we employ Shin's 2024 result to prove a q-skew Amitsur's theorem whenever the field is additionally assumed to be of characteristic zero. That is, the Jacobson radical of $R[x;σ, δ]$ is $N[x;σ,δ]$ for some nil ideal $N$ of $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a $q$-Skew Amitsur's Theorem Launois, Aristide F. J. -C. Rings and Algebras 16N20, 16N40 Let $R$ be an algebra over an uncountable field, $σ$ a locally torsion automorphism and $δ$ a locally nilpotent left $σ$-derivation such that $qσδ= δσ$, where $q$ is a nonzero scalar. We show that the constant part of the Jacobson radical of the Ore extension $R[x;σ,δ]$ is nil. This partially answers a question of Greenfeld, Smoktunowicz and Ziembowski posed in 2019. As a corollary, we employ Shin's 2024 result to prove a q-skew Amitsur's theorem whenever the field is additionally assumed to be of characteristic zero. That is, the Jacobson radical of $R[x;σ, δ]$ is $N[x;σ,δ]$ for some nil ideal $N$ of $R$. |
| title | On a $q$-Skew Amitsur's Theorem |
| topic | Rings and Algebras 16N20, 16N40 |
| url | https://arxiv.org/abs/2605.08100 |