Glasnik matematički, Vol. 53 No. 1, 2018.
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
Publication date:
20.6.2018.
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