Glasnik Matematicki, Vol. 56, No. 1 (2021), 95-106.

A RESULT RELATED TO DERIVATIONS ON UNITAL SEMIPRIME RINGS

Irena Kosi-Ulbl, Nejc Širovnik and Joso Vukman

Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
e-mail: irena.kosi@um.si

WinSystems, Global Gaming Solutions Partner
e-mail: nejc.sirovnik@gmail.com

Faculty of Natural Sciences and Mathematics, Department of Mathematics and Computer Science, University of Maribor, Koroška 160, 2000 Maribor, Slovenia
e-mail: joso.vukman@guest.um.si

Abstract.   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.

2010 Mathematics Subject Classification.   16N60, 39B52

Key words and phrases.   Prime ring, semiprime ring, derivation, Jordan derivation

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https://doi.org/10.3336/gm.56.1.07

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