Abstract
In this paper we prove that left multiplicative generalized Jordan derivation and left multiplicative generalized Jordan triple derivation of 2-torsion free semiprime rings are left multiplicative generalized derivation.
Highlights
Bresar [1] has proved that any Jordan triple derivation on 2-torsion free semiprime ring is a derivation
Since R is a semiprime ring one can conclude that D is a derivation
One can conclude that T is a right centralizer in ref
Summary
Bresar [1] has proved that any Jordan triple derivation on 2-torsion free semiprime ring is a derivation. Let R be a 2-torsion free semiprime ring and let F:R→R be a left multiplicative generalized Jordan derivation. Proof: We have the relation, F(x2)=xF(x)+D(x)x, for all x∈R. Since R is a semiprime ring one can conclude that D is a derivation.
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