Annihilating condition of $b$-generalized skew derivations with central values in prime rings
Basudeb DHARA, Sukhendu KAR, Kalyan SINGH
Received May 26, 2025. Published online March 30, 2026.
Abstract: Let $\mathcal{R}$ be any prime ring of char$(\mathcal{R})\neq2$ with extended centroid $\mathcal{C}$, $\mathcal{Q}_r$ its right Martindale quotient ring, $f(\zeta_1,\ldots,\zeta_n)$ a noncentral multilinear polynomial over $\mathcal{C}$ and $p,q \in\mathcal{Q}_r$ fixed nonzero elements. If $\mathcal{F}$ is any $b$-generalized skew derivation of $\mathcal{R}$ satisfying the condition $p\mathcal{F}(f(\zeta_1,\ldots,\zeta_n))f(\zeta_1,\ldots,\zeta_n)q\in\mathcal{C}$ for all $\zeta_1,\ldots,\zeta_n\in\mathcal{R}$, then the nature of the map $\mathcal{F}$ is described. The result completes the incomplete result of N. Rehman, S. A. Pary, and J. Nisar (2023).
Keywords: derivation; $b$-generalized skew derivation; multilinear polynomial; prime ring
Affiliations: Basudeb Dhara (corresponding author), Department of Mathematics, Natural Science Research Center of Belda College under Vidyasagar University, Belda, Paschim Medinipur, 721424, West Bengal, India, e-mail: basu_dhara@yahoo.com; Sukhendu Kar, Kalyan Singh, Department of Mathematics, Jadavpur University, 188, Raja S.C. Mallick Road, Kolkata, 700032, West Bengal, India, e-mail: karsukhendu@yahoo.co.in, kalyank4singh@gmail.com
