GENERALIZED JORDAN TRIPLE $(\theta,\phi)$-DERIVATIONS ON SEMIPRIME RINGS

Abstract

Let $R$ be a 2-torsion free semiprime ring. In this paper we will show that every Jordan triple $(\theta,\phi)$-derivation on $R$ is a $(\theta,\phi)$-derivation. Also every Jordan triple left centralizer on $R$ is a left centralizer. As a consequence, every generalized Jordan triple $(\theta,\phi)$-derivation on $R$ is a generalized $(\theta,\phi)$-derivation. This result gives an affirmative answer to the question posed by Wu and Lu in [14].