### Maja Fošner and Nina Peršin

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

Prušnikova 48, 2000 Maribor, Slovenia
e-mail: nina-persin@t-2.net

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 R be a prime ring with char(R)=0 or 4 < char(R), and let D:R → R be an additive mapping satisfying either the relation D(x3)=D(x2)x+x2D(x) or the relation D(x3)=D(x)x2+xD(x2) for all x R. In both cases D is a derivation.

2010 Mathematics Subject Classification.   16W10, 46K15, 39B05.

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

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DOI: 10.3336/gm.48.1.06

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