A NOTE ON LIE IDEALS OF PRIME RINGS

Abstract

Let R be a 2-torsion free prime ring, U a nonzero Lie ideal of R such that u 2 2 U for all u 2 U. In the present paper, it is proved that if d is a nonzero derivation and ((d(u),u),u) = 0 for all u 2 U, then U µ Z(R). Moreover, suppose that d1,d2,d3 are nonzero derivations of R such that d3(y)d1(x) = d2(x)d3(y) for all x,y 2 U, then U µ Z(R). Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the above results are not superfluous.