### Ajda Fošner, Maja Fošner and Joso Vukman

Faculty of Management, University of Primorska, Cankarjeva 5, 6104 Koper, Slovenia
e-mail: ajda.fosner@fm-kp.si

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

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

Abstract.   In this paper we investigate identities with derivations in rings. We prove, for example the following result. Let m ≥ 1,n ≥ 1 be some fixed integers and let R be a 6nm2(2m+n-3)!-torsion free semiprime ring. Suppose there exists a derivation D:R → R satisfying the relation [[D(xm),xn] ,D(xm)]=0 for all x R. In this case D maps R into its center.

2000 Mathematics Subject Classification.   16N60.

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

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DOI: 10.3336/gm.46.2.06

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