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 $u,v \in U$.
@article{107732,
author = {Mohammad Ashraf and Nadeem-ur-Rehman},
title = {On Lie ideals and Jordan left derivations of prime rings},
journal = {Archivum Mathematicum},
volume = {036},
year = {2000},
pages = {201-206},
zbl = {1030.16018},
mrnumber = {1785037},
language = {en},
url = {http://dml.mathdoc.fr/item/107732}
}
Ashraf, Mohammad; Nadeem-ur-Rehman. On Lie ideals and Jordan left derivations of prime rings. Archivum Mathematicum, Tome 036 (2000) pp. 201-206. http://gdmltest.u-ga.fr/item/107732/
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