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Generalized derivations with nilpotent values on Lie ideals in semiprime rings

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Abstract

Let R be a prime ring of characteristic different from 2, \(Q_r\) its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R, \(n\ge 1\) a fixed integer, F and G two generalized derivations of R. If \(\bigl (F(xy)-G(x)G(y)\bigr )^n=0\), for any \(x,y \in L\), then there exists \(\lambda \in C\) such that \(F(x)=\lambda ^2 x\) and \(G(x)=\lambda x\), for any \(x\in R\). Moreover, we analyze the semiprime case.

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Authors and Affiliations

  1. MIFT, University of Messina, 98166, Messina, Italy

    Francesco Ammendolia

  2. Department of Engineering, University of Messina, 98166, Messina, Italy

    Giovanni Scudo

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  1. Francesco Ammendolia
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  2. Giovanni Scudo
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Correspondence to Giovanni Scudo.

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Ammendolia, F., Scudo, G. Generalized derivations with nilpotent values on Lie ideals in semiprime rings. Beitr Algebra Geom (2023). https://doi.org/10.1007/s13366-023-00715-w

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