Multilinear polynomial identities under the action of generalized skew derivations
UDC 512.552 Suppose that $\mathcal{H}_1, \mathcal{H}_2$ and $\mathcal{H}_3$ are generalized skew derivations on prime ring $\mathcal{R}$ with ${\rm char}(\mathcal{R})\neq 2$ such that $\mathcal{H}_1\big(\mathcal{H}_2(\pi(q))\pi(q)\big)=\mathcal{H}_3(\pi(q)^2)$ for all $q=(q_1,\ldots,q_n) \in \mathca...
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| Date: | 2026 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9591 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 512.552
Suppose that $\mathcal{H}_1, \mathcal{H}_2$ and $\mathcal{H}_3$ are generalized skew derivations on prime ring $\mathcal{R}$ with ${\rm char}(\mathcal{R})\neq 2$ such that $\mathcal{H}_1\big(\mathcal{H}_2(\pi(q))\pi(q)\big)=\mathcal{H}_3(\pi(q)^2)$ for all $q=(q_1,\ldots,q_n) \in \mathcal{R}^n,$ where $\pi(q_1,\ldots,q_n)$ denotes the multilinear polynomial over $\mathcal{C},$ which is noncentral and nonidentity. We present all possible configurations of the maps $\mathcal{H}_1, \mathcal{H}_2,$ and $\mathcal{H}_3.$ This extends the results obtained by V. de Filippis [Comm. Algebra, 49, No. 7, 2987–3009 (2021)]. |
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| DOI: | 10.3842/umzh.v78i7-8.9591 |