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2024 | OriginalPaper | Chapter

A Note on $\textrm{b}$-Generalized Skew Derivations on Prime Rings

Authors : Mani Shankar Pandey, Ashutosh Pandey

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

Let $\mathcal {R}$ be a prime ring with a characteristic not equal to 2. Let $\mathcal {U}$ and $\mathcal {C}$ denote its Utumi quotient ring and extended centroid, respectively. Consider a non-central multilinear polynomial $\phi (\zeta _1, \ldots , \zeta _n)$ over $\mathcal {C}$, and let $\textbf{G}$ be a $\textrm{b}$-generalized skew derivation of $\mathcal {R}$, satisfying the identity:

$$ p \phi (\zeta )\textbf{G}(\phi (\zeta ))= \textbf{G}(\phi (\zeta )^2),\ p\ne 2,\ \forall \ \zeta =(\zeta _1\ldots ,\zeta _n)\in \mathcal {R}^n.$$

The purpose of this paper is to classify all potential forms of the $\textrm{b}$-generalized skew derivation $\textbf{G}.$

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previous chapter Commutativity of -Prime Rings with Generalized Derivation

next chapter Analysis of Some Topological Indices Over the Weakly Zero-Divisor Graph of the Ring

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Title: A Note on -Generalized Skew Derivations on Prime Rings
Authors: Mani Shankar Pandey
Ashutosh Pandey
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_7

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A Note on \(\textrm{b}\)-Generalized Skew Derivations on Prime Rings

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