GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS

Abstract

It is shown that, given a 2-torsion-free semiprime ring with unit e, every generalized Jordan derivation on TZ is a generalized derivation.Let n be a fixed positive integer, TZ be a noncommutative (n + l)!-torsion-free prime ring with the center Cn-It is proved that, if // : TZ -» TZ is a generalized Jordan derivation of TZ such that ¡i(x)x n +x n fi{x) € Cn for all x € TZ, then fx = 0.