Remarks on Certain Identities with Derivations on Semiprime Rings

  • N. Baydar
  • A. Fošner
  • R. Strašek

Abstract

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 $x Є R$, 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 x ∈ R, where $F(x) = (D_1^2 (x) + D_2(x)) ∘ α(x),\; x ∈ R$, and $β$ is any automorphism or antiautomorphism on $R$.
Published
25.10.2014
How to Cite
Baydar N., FošnerA., and StrašekR. “Remarks on Certain Identities With Derivations on Semiprime Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 10, Oct. 2014, pp. 1436–1440, http://umj.imath.kiev.ua/index.php/umj/article/view/2236.
Section
Short communications