International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 18, Pages 53145, 13 p.
doi:10.1155/IJMMS/2006/53145

Products of derivations which act as Lie derivations on commutators of right ideals.

Abstract

Let R be a prime ring of characteristic different from 2, I a nonzero right ideal of R, d and δ nonzero derivations of R, and s4(x1,x2,x3,x4) the standard identity of degree 4. If the composition (dδ) is a Lie derivation of [I,I] into R, then either s4(I,I,I,I)I=0 or δ(I)I=d(I)I=0.