International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 170749, 5 pages
http://dx.doi.org/10.1155/2013/170749
Research Article

Generalized Derivations on Prime Near Rings

Asma Ali,1 Howard E. Bell,2 and Phool Miyan1

1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2Department of Mathematics, Brock University, St. Catharines, ON, Canada L2S 3A1

Received 8 October 2012; Accepted 2 January 2013

Academic Editor: Christian Corda

Copyright © 2013 Asma Ali et al. 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 be a near ring. An additive mapping is said to be a right generalized (resp., left generalized) derivation with associated derivation on if (resp., ) for all . A mapping is said to be a generalized derivation with associated derivation on if is both a right generalized and a left generalized derivation with associated derivation on . The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.