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Generalized derivations as Jordan homomorphisms on lie ideals and right ideals

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Abstract

Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g(x) = x for all x ∈ R, or char(R) = 2, R satisfies the standard identity s 4(x 1, x 2, x 3, x 4), L is commutative and u 2 ∈ Z(R), for any u ∈ L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R.

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  1. DI.S.I.A., University of Messina, Faculty of Engineering Contrada di Dio, 98166, Messina, Italy

    Vincenzo de Filippis

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  1. Vincenzo de Filippis
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Correspondence to Vincenzo de Filippis.

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de Filippis, V. Generalized derivations as Jordan homomorphisms on lie ideals and right ideals. Acta. Math. Sin.-English Ser. 25, 1965–1974 (2009). https://doi.org/10.1007/s10114-009-7343-0

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  • DOI: https://doi.org/10.1007/s10114-009-7343-0

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