LIE IDEAL AND GENERALIZED JORDAN LEFT DERIVATION ON SEMIPRIME RINGS

Abstract

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 Q_r(S) is the Martindale quotient ring of S then there exists q ∈ Q_r(S) such that g(x) = qx + d(x) for all x ∈ R. (In right derivation case).