Abstract
In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u 2 ∈ U, for all u ∈ U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U ⫅Z(R).
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References
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Asma, A., Rehman, N. & Shakir, A. On Lie ideals with derivations as homomorphisms and anti-homomorphisms. Acta Mathematica Hungarica 101, 79–82 (2003). https://doi.org/10.1023/B:AMHU.0000003893.61349.98
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DOI: https://doi.org/10.1023/B:AMHU.0000003893.61349.98