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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 53145, 13 pages
http://dx.doi.org/10.1155/IJMMS/2006/53145

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

Dipartimento di Matematica, Universitá di Messina, Salita Sperone 31, Messina 98166, Italy

Received 5 April 2006; Revised 22 October 2006; Accepted 30 October 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.