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 |
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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| _version_ | 1871646579087114240 |
|---|---|
| author | Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet |
| author_facet | Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet |
| author_institution_txt_mv | [
{
"author": "Pallavee Gupta",
"institution": "Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Katpadi, India"
},
{
"author": "S. K. Tiwari",
"institution": "Department of Mathematics, Indian Institute of Technology Patna, Bihar, India"
},
{
"author": "Lovepreet Singh",
"institution": "Department of Mathematics, Indian Institute of Technology Patna, Bihar, India"
}
] |
| author_sort | Gupta, Pallavee |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:12Z |
| description | 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)]. |
| doi_str_mv | 10.3842/umzh.v78i7-8.9591 |
| first_indexed | 2026-07-25T01:01:11Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9591 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:01:11Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-95912026-07-24T15:24:12Z Multilinear polynomial identities under the action of generalized skew derivations Multilinear polynomial identities under the action of generalized skew derivations Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet Prime ring Generalized skew derivation The right Martindale quotient ring Extended centroid Prime ring Generalized skew derivation Right Martindale Quotient ring Extended Centroid 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)]. УДК 512.552 Мультилінійні поліноміальні тотожності під дією узагальнених косих диференціювань Припустимо, що $\mathcal{H}_1, \mathcal{H}_2$ та $\mathcal{H}_3$ – узагальнені косі диференціювання на первинному кільці $\mathcal{R}$ із характеристикою ${\rm char}(\mathcal{R})\neq 2$ такі, що $\mathcal{H}_1 \big(\mathcal{H}_2(\pi(q))\pi(q)\big)=\mathcal{H}_3(\pi(q)^2)$ для всіх $q=(q_1,\ldots,q_n)\in\mathcal{R}^n,$ де $\pi(q_1,\ldots,q_n)$ позначає мультилінійний поліном над $\mathcal{C},$ який не є ні центральним, ні тотожно нульовим. Описано всі можливі конфігурації відображень $\mathcal{H}_1, \mathcal{H}_2$ та $\mathcal{H}_3.$ Отримані результати узагальнюють результати Філіппіса [V. de Filippis, Comm. Algebra, 49, № 7, 2987–3009 (2021)]. Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9591 10.3842/umzh.v78i7-8.9591 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 605 Український математичний журнал; Том 78 № 7-8 (2026); 605 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9591/10686 Copyright (c) 2026 Pallavee Gupta, S. K. Tiwari, Lovepreet Singh |
| spellingShingle | Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet Gupta, Pallavee Tiwari, S. K. Singh, Lovepreet Multilinear polynomial identities under the action of generalized skew derivations |
| title | Multilinear polynomial identities under the action of generalized skew derivations |
| title_alt | Multilinear polynomial identities under the action of generalized skew derivations |
| title_full | Multilinear polynomial identities under the action of generalized skew derivations |
| title_fullStr | Multilinear polynomial identities under the action of generalized skew derivations |
| title_full_unstemmed | Multilinear polynomial identities under the action of generalized skew derivations |
| title_short | Multilinear polynomial identities under the action of generalized skew derivations |
| title_sort | multilinear polynomial identities under the action of generalized skew derivations |
| topic_facet | Prime ring Generalized skew derivation The right Martindale quotient ring Extended centroid Prime ring Generalized skew derivation Right Martindale Quotient ring Extended Centroid |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9591 |
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