%0 Journal Article
%T A result in the spirit of Herstein theorem
%A Fo£¿ner
%A Maja
%A Marcen
%A Benjamin
%A Vukman
%A Joso
%J -
%D 2018
%R 10.3336/gm.53.1.06
%X Sa£¿etak A classical result of Herstein asserts that any Jordan derivation on a prime ring of characteristic different from two is a derivation. It is our aim in this paper to prove the following result, which is in the spirit of Herstein's theorem. Let \(n¡Ý 3\) be some fixed integer, let R be a prime ring with \(char(R)> 4n-8\) and let D:R ¡ú R be an additive mapping satisfying either the relation \(D(x^n)=D(x^{n-1})x+x^{n-1}D(x)\) or the relation \(D(x^n)=D(x)x^{n-1}+xD(x^{n-1})\) for all \(x \in R\). In both cases D is a derivation
%K Prime ring
%K semiprime ring
%K derivation
%K Jordan derivation
%K functional identity
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=297048