Glasnik matematički, Vol. 46 No. 2, 2011.
Original scientific paper
https://doi.org/10.3336/gm.46.2.06
Identities with derivations in rings
Ajda Fošner
; Faculty of Management, University of Primorska, Cankarjeva 5, 6104 Koper, Slovenia
Maja Fošner
; Faculty of Logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Joso Vukman
; Department of Mathematics and Computer Science, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
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.
Keywords
Prime ring; semiprime ring; derivation
Hrčak ID:
74264
URI
Publication date:
23.11.2011.
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