Glasnik matematički, Vol. 56 No. 1, 2021.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.56.1.07
A result related to derivations on unital semiprime rings
Irena Kosi-Ulbl
orcid.org/0000-0002-9908-0877
; Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
Nejc Širovnik
; WinSystems, Global Gaming Solutions Partner
Joso Vukman
; Faculty of Natural Sciences and Mathematics, Department of Mathematics and Computer Science, University of Maribor, Koroška 160, 2000 Maribor, Slovenia
Sažetak
The purpose of this paper is to prove the following result. Let n≥3 be some fixed integer and let R be a (n+1)!2n-2-torsion free semiprime unital ring. Suppose there exists an additive mapping D: R→ R satisfying the relation
for all x ∈ R. In this case D is a derivation. The history of this result goes back to a classical result of Herstein, which states that any Jordan derivation on a 2-torsion free prime ring is a derivation.
Ključne riječi
Prime ring, semiprime ring, derivation, Jordan derivation
Hrčak ID:
259303
URI
Datum izdavanja:
24.6.2021.
Posjeta: 528 *