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On b-generalized derivations in prime rings

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Abstract

Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, \(f\left( x_1,\ldots ,x_n\right)\) be a multilinear polynomial over C, which is not central valued on R. Suppose F, G are non zero b-generalized derivations of R such that \(puF(u)+F(u)uq=G\left( u^2\right)\), \(p+q \notin C\) for all \(u\in f(R)\). Then we describe all the possible representations of F, G.

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Acknowledgements

I want to express my gratitude to my guide, Dr. Balchand Prajapati, for his unwavering assistance, advice, and encouragement. There is no conflict of interest between the guide and the author.

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  1. School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, 110006, India

    Charu Gupta

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  1. Charu Gupta
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Gupta, C. On b-generalized derivations in prime rings. Rend. Circ. Mat. Palermo, II. Ser 72, 2703–2720 (2023). https://doi.org/10.1007/s12215-022-00817-9

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