Original scientific paper

https://doi.org/10.3336/gm.53.1.06

A result in the spirit of Herstein theorem

Maja Fošner ; Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Benjamin Marcen ; Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Joso Vukman ; Institute of mathematics, physics and mechanics, Jadranska 19, 1000 Ljubljana, Slovenia

Abstract

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 \(n≥ 3\) be some fixed integer, let R be a prime ring with \(char(R)> 4n-8\) and let D:R → 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.

Keywords

Prime ring; semiprime ring; derivation; Jordan derivation; functional identity

Hrčak ID:

201813

URI

https://hrcak.srce.hr/201813

Publication date:

20.6.2018.

Visits: 904 *