International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 53-56, Pages 2895-2906
doi:10.1155/S0161171204311221
On dependent elements in rings.
Joso Vukman
and Irena Kosi-Ulbl
Department of Mathematics, University of Maribor, Koro {s}ka cesta 160, Maribor 2000, Slovenia
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.