### Maja Fošner, Benjamin Marcen and Joso Vukman

Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
e-mail: maja.fosner@um.si

Faculty of logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
e-mail: benjamin.marcen@um.si

Institute of mathematics, physics and mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
e-mail: joso.vukman@guest.um.si

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(xn)=D(xn-1)x+xn-1D(x) or the relation D(xn)=D(x)xn-1+xD(xn-1) for all x R. In both cases D is a derivation.

2010 Mathematics Subject Classification.   16W10, 39B05.

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

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DOI: 10.3336/gm.53.1.06

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