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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 17, Pages 2703-2710
http://dx.doi.org/10.1155/IJMMS.2005.2703

On some equations related to derivations in rings

Department of Mathematics, Faculty of Education (PEF), University of Maribor, Koroška 160, Maribor 2000, Slovenia

Received 30 December 2004; Revised 21 July 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let m and n be positive integers with m+n0, and let R be an (m+n+2)!-torsion free semiprime ring with identity element. Suppose there exists an additive mapping D:RR, such that D(xm+n+1)=(m+n+1)xmD(x)xn is fulfilled for all xR, then D is a derivation which maps R into its center.