ON LIE IDEALS AND JORDAN LEFT DERIVATIONS OF PRIME RINGS

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