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International Journal of Mathematics and Mathematical Sciences
Volume 2008, Article ID 490316, 5 pages
Research Article

On Prime Near-Rings with Generalized Derivation

Department of Mathematics, Faculty of Mathematics and Science, Brock University, St. Catharines, Ontario, Canada L2S 3A1

Received 29 November 2007; Accepted 25 February 2008

Academic Editor: Francois Goichot

Copyright © 2008 Howard E. Bell. 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 𝑁 be a 3-prime 2-torsion-free zero-symmetric left near-ring with multiplicative center 𝑍. We prove that if 𝑁 admits a nonzero generalized derivation 𝑓 such that 𝑓(𝑁)𝑍, then 𝑁 is a commutative ring. We also discuss some related properties.