Geodesic
On Lie ideals and Jordan left derivations of prime rings
Archivum mathematicum, Tome 36 (2000) no. 3, pp. 201-206.

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Let $R$ be a 2-torsion free prime ring and let $U$ be a Lie ideal of $R$ such that $u^{2} \in U$ for all $u \in U$. In the present paper it is shown that if $d$ is an additive mappings of $R$ into itself satisfying $d(u^{2})=2ud(u)$ for all $u \in U$, then $d(uv)=ud(v)+vd(u)$ for all $u,v \in U$.
Classification : 16N60, 16W10, 16W25
Keywords: Lie ideals; prime rings; Jordan left derivations; left derivations; torsion free rings 
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     title = {On {Lie} ideals and {Jordan} left derivations of prime rings},
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Ashraf, Mohammad; Nadeem-ur-Rehman. On Lie ideals and Jordan left derivations of prime rings. Archivum mathematicum, Tome 36 (2000) no. 3, pp. 201-206. http://geodesic.mathdoc.fr/item/ARM_2000__36_3_a4/