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ON LIE IDEALS AND JORDAN LEFT DERIVATIONS OF PRIME RINGS

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*Mohammad Ashraf and Nadeem-ur-Rehman*

**Address.** M. Ashraf, Department of Mathematics, Faculty of Science,
King Abdul Aziz University, P.O. Box. 9028, Jeddah 21413, SAUDI-ARABIA
Nadeem-ur-Rehman, Department of Mathematics, Aligarh Muslim University,
Aligarh 202002, INDIA

**Abstract.** 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 $u,v \in U$.

**AMSclassification.** 16W25, 16N60

**Keywords.** Lie ideals, prime rings, Jordan left derivations, left
derivations, torsion free rings