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Ukrainian Mathematical Journal

, Volume 66, Issue 10, pp 1609–1614 | Cite as

Remarks on Certain Identities with Derivations on Semiprime Rings

  • A. Fošner
  • N. Baydar
  • R. Strašek
Article
  • 93 Downloads

Let n be a fixed positive integer, let R be a (2n)! -torsion-free semiprime ring, let \( \alpha \) be an automorphism or an anti-automorphism of R, and let D 1 , D 2 : R → R be derivations. We prove the following result: If (D 1 2 (x) + D 2(x)) n  ∘ α(x) n  = 0 holds for all xR, then D 1 = D 2 = 0. The same is true if R is a 2-torsion free semiprime ring and F(x) ° β(x) = 0 for all xR, where F(x) = (D 1 2 (x) + D 2(x)) ∘ α(x), x ∈ R, and β is any automorphism or antiautomorphism on R.

Keywords

Positive Integer Additive Mapping Prime Ring Associative Ring Semiprime Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. Fošner
    • 1
  • N. Baydar
    • 2
  • R. Strašek
    • 1
  1. 1.University of PrimorskaKoperSlovenia
  2. 2.Ege UniversityIzmirTurkey

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