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On Prime Near-Rings with Generalized Derivation

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  • Howard E. Bell

Abstract

Let ð ‘ be a 3-prime 2-torsion-free zero-symmetric left near-ring with multiplicative center ð ‘ . We prove that if ð ‘ admits a nonzero generalized derivation ð ‘“ such that ð ‘“ ( ð ‘ ) ⊆ ð ‘ , then ð ‘ is a commutative ring. We also discuss some related properties.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:490316
    DOI: 10.1155/2008/490316
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    Cited by:

    1. Ahmed A. M. Kamal & Khalid H. Al-Shaalan, 2013. "Commutativity of rings and near-rings with generalized derivations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(4), pages 473-496, August.
    2. Asma Ali & Howard E. Bell & Phool Miyan, 2013. "Generalized Derivations on Prime Near Rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-5, February.
    3. 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.
    4. Khalid H. Al-Shaalan, 2017. "On commutativity of near-rings with generalized derivations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(2), pages 259-269, June.

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