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Siberian Mathematical Journal

, Volume 46, Issue 2, pp 270–275 | Cite as

Some properties of prime near-rings with (σ,τ)-derivation

  • O. Golbasi
Article

Abstract

Some results by Bell and Mason on commutativity in near-rings are generalized. Let N be a prime right near-ring with multiplicative center Z and let D be a (σ,τ)-derivation on N such that σD = Dσ and τD = Dτ. The following results are proved: (i) If D(N) ⊂ Z or [D(N), D(N)] = 0 or [D(N), D(N)]σ,τ = 0 then (N, +) is abelian; (ii) If D(xy) = D(x)D(y) or D(xy) = D(y)D(x) for all x, yN then D = 0.

Keywords

prime near-ring derivation (σ τ)-derivation 

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References

  1. 1.
    Bell H. E. and Mason G., “On derivations in near-rings,” in: Near-Rings and Near-Fields, North-Holland, Amsterdam (1987). (Math. Studies; 137.)Google Scholar
  2. 2.
    Bell H. E. and Kappe L. C., “Rings in which derivations satisfy certain algebraic conditions,” Acta Math. Hungar., 53, No.3–4, 339–346 (1989).Google Scholar
  3. 3.
    Argafic N., “On prime and semiprime near-rings with derivations,” Internat. J. Math. Math. Sci., 20, No.4, 737–740 (1997).CrossRefGoogle Scholar
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    Pilz G., Near-Rings, North-Holland, Amsterdam (1983).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • O. Golbasi
    • 1
  1. 1.Cumhuriyet UniversitySivasTurkey

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