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On Generalized Semiderivations of Prime Near Rings

Author

Listed:
  • Abdelkarim Boua
  • A. Raji
  • Asma Ali
  • Farhat Ali

Abstract

Let be a near ring. An additive mapping is said to be a generalized semiderivation on if there exists a semiderivation associated with a function such that and for all . In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ring .

Suggested Citation

  • Abdelkarim Boua & A. Raji & Asma Ali & Farhat Ali, 2015. "On Generalized Semiderivations of Prime Near Rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-7, November.
    • Handle: RePEc:hin:jijmms:867923
    DOI: 10.1155/2015/867923
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    References listed on IDEAS

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    1. Howard E. Bell, 2008. "On Prime Near-Rings with Generalized Derivation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-5, April.
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