Semiprime Г-rings with Jordan Derivations

Abstract

Let M be a 2-torsion free semiprime Г-ring and d:M→M a Jordan left derivation. We find the existence of a positive integer n with the condition 􁈺d􁈺x􁈻α􁈻􀭬d(x)=0, for all x􀗐 M and α􀗐 Г, which gives d=0. With the help of this assertion, we show that the presence of Jordan derivations d and g on the 2-torsion free Г-ring M such that d􀬶(x)=g(x), for all x􀗐 M implies d=0.