Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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STRUCTURE OF 3-PRIME NEAR-RINGS SATISFYING SOME IDENTITIES

  • Boua, Abdelkarim (Sidi Mohammed Ben Abdellah University Polydisciplinary Faculty)
  • Received : 2017.11.07
  • Accepted : 2018.04.11
  • Published : 2019.01.31
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Abstract

In this paper, we investigate commutativity of 3-prime near-rings ${\mathcal{N}}$ in which (1, ${\alpha}$)-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of 3-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.

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References

  1. M. Ashraf, A. Ali, and S. Ali, (${\sigma}$, ${\tau}$)-derivations on prime near rings, Arch. Math. (Brno) 40 (2004), no. 3, 281-286.
  2. M. Ashraf and S. Ali, On (${\sigma}$, ${\tau}$)-derivations of prime near-rings. II, Sarajevo J. Math. 4(16) (2008), no. 1, 23-30.
  3. H. E. Bell, On derivations in near-rings. II, in Nearrings, nearfields and K-loops (Hamburg, 1995), 191-197, Math. Appl., 426, Kluwer Acad. Publ., Dordrecht, 1997.
  4. H. E. Bell, A. Boua, and L. Oukhtite, Semigroup ideals and commutativity in 3-prime near rings, Comm. Algebra 43 (2015), no. 5, 1757-1770. https://doi.org/10.1080/00927872.2013.879161
  5. H. E. Bell and G. Mason, On derivations in near-rings, in Near-rings and near-fields (Tubingen, 1985), 31-35, North-Holland Math. Stud., 137, North-Holland, Amsterdam, 1987.
  6. A. Boua and L. Oukhtite, Semiderivations satisfying certain algebraic identities on prime near-rings, Asian-Eur. J. Math. 6 (2013), no. 3, 1350043, 8 pp.
  7. O. Golbasi and N. Aydin, Results on prime near-ring with (${\sigma}$, ${\tau}$)-derivation, Math. J. Okayama Univ. 46 (2004), 1-7.
  8. A. A. M. Kamal, ${\sigma}$-derivations on prime near-rings, Tamkang J. Math. 32 (2001), no. 2, 89-93. https://doi.org/10.5556/j.tkjm.32.2001.349
  9. G. Pilz, Near-Rings, 2nd ed., North Holland /American Elsevier, Amsterdam, 1983.
  10. M. S. Samman, L. Oukhtite, A. Raji, and A. Boua, Two sided ${\alpha}$-derivations in 3-prime near-rings, Rocky Mountain J. Math. 46 (2016), no. 4, 1379-1393. https://doi.org/10.1216/RMJ-2016-46-4-1379
  11. X. K.Wang, Derivations in prime near-rings, Proc. Amer. Math. Soc. 121 (1994), no. 2, 361-366. https://doi.org/10.1090/S0002-9939-1994-1181177-7