Remarks on Certain Identities with Derivations on Semiprime Rings

• Date: 2014
• Main Authors: Baydar, N., Fošner, A., Strašek, R., Байдар, Н., Фоснер, А., Страшек, Р.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2236
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $...