LIE IDEAL AND GENERALIZED JORDAN LEFT DERIVATION ON SEMIPRIME RINGS - Sharma, R.K.; Prajapati, B. (Italian Journal of Pure and Applied Mathematics, 2013)
Let R be a 2-torsion free semiprime ring in which x2 = 0 implies x = 0. Let g be a generalized Jordan left (right) derivation associated with Jordan left (right) derivation d on R. Then g is a generalized left (right) derivation on R. It is proved that if Qr(S) is the Martindale quotient ring of S then there exists q ∈ Qr(S) such that g(x) = qx + d(x) for all x ∈ R. (In right derivation case).