International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 54, Pages 2895-2906
doi:10.1155/S0161171204311221
On dependent elements in rings
Department of Mathematics, University of Maribor, Koroška cesta 160, Maribor 2000, Slovenia
Received 18 November 2003
Copyright © 2004 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 R be an associative ring. An element a∈R is said to be dependent on a mapping F:R→R in case F(x)a=ax holds for all x∈R. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ring R, there are no nonzero elements which are dependent on the mapping α+β, where α and β are automorphisms of R.