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International Journal of Mathematics and Mathematical Sciences 
Volume 2008 (2008), Article ID 490316, 5 pages
doi:10.1155/2008/490316

Research Article

On Prime Near-Rings with Generalized Derivation

Howard E. Bell

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

Received 29 November 2007; Accepted 25 February 2008

Recommended by Francois Goichot

Abstract

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.