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Commutativity of rings and near-rings with generalized derivations

Author

Listed:
  • Ahmed A. M. Kamal

    (King Saud University)

  • Khalid H. Al-Shaalan

    (King Abdul-aziz Military Academy)

Abstract

In this paper we prove some theorems of commutativity for prime rings or 3-prime near-rings with a suitably constrained generalized derivation. As a consequence of the results obtained, we prove several commutativity theorems for 3-prime near-rings and prime rings. Also, we prove some other results about the generalized derivation either on a near-ring or on a ring.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:44:y:2013:i:4:d:10.1007_s13226-013-0025-8
    DOI: 10.1007/s13226-013-0025-8
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    References listed on IDEAS

    as
    1. Ahmed A. M. Kamal & Khalid H. Al-Shaalan, 2012. "Commutativity of near-rings with derivations by using algebraic substructures," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(3), pages 211-225, June.
    2. 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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    Cited by:

    1. 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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