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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 70, Pages 3859-3865

On derivations and commutativity in prime rings

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

Received 29 March 2004

Copyright © 2004 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.


Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x),x],[d(y),y]]=0, for all x,yI. We prove that if [I,I]I0, then d(I)I=0.