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On a quadratic differential identity with b-generalized derivations.

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Abstract

Let R be a prime ring of characteristic different from 2, with right Martindale quotient ring \(Q_r\) and extended centroid C, L a non-central Lie ideal of R, F a non-zero b-generalized derivation of R and \(\delta \) a non-zero derivation of R, such that \([F(u),\delta (u)]=0\), for all \(u \in L\). Then F is a derivation of R and there exists \(\lambda \in C\) such that \(F=\lambda \delta \), unless when R satisfies the standard identity \(s_4(x_1,\ldots ,x_4)\).

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  1. Department of Law, Economics and Sociology, Magna Græcia University of Catanzaro, Viale Europa Loc. Germaneto, 88100, Catanzaro, Italy

    Francesco Rania

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  1. Francesco Rania
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Rania, F. On a quadratic differential identity with b-generalized derivations.. Ann Univ Ferrara 70, 359–368 (2024). https://doi.org/10.1007/s11565-023-00475-4

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