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2024 | OriginalPaper | Chapter

Generalized Skew-Derivations Acting on Multilinear Polynomials in Prime Rings

Authors : Manami Bera, Basudeb Dhara

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

Let R be a noncommutative prime ring of characteristic different from 2, $Q_r$ be its right Martindale quotient ring, C be its extended centroid and $f(r_1,\ldots ,r_n)$ be a noncentral multilinear polynomial over C. Suppose that $T_1$, $T_2$ are two generalized skew derivations on R. If

$$\begin{aligned} T_1(u)T_2(u)=T_1(u)u-uT_2(u)\end{aligned}$$

for all $u\in f(R)=\{f(x_1,\ldots ,x_n) | x_1,\ldots ,x_n\in R\}$, then we determine all possible forms of the maps.

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previous chapter Generalized Skew Derivations with Periodic Values on Lie Ideals

next chapter Results on b-Generalized Derivations in Rings

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Title: Generalized Skew-Derivations Acting on Multilinear Polynomials in Prime Rings
Authors: Manami Bera
Basudeb Dhara
Publisher: Springer Nature Switzerland
Book: Advances in Ring Theory and Applications
Print ISBN: 978-3-031-50794-6

Electronic ISBN: 978-3-031-50795-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50795-3_20

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