International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2703-2710
doi: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 Joso Vukman and Irena Kosi-Ulbl. 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+n≠0, and let R be an (m+n+2)!-torsion free semiprime ring with identity element. Suppose there exists an additive mapping D:R→R, such that D(xm+n+1)=(m+n+1)xmD(x)xn is fulfilled for all x∈R, then D is a derivation which maps R into its center.