International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1031-1038
doi:10.1155/IJMMS.2005.1031
Identities with derivations and automorphisms on semiprime rings.
Joso Vukman
Department of Mathematics, Faculty of Education, University of Maribor, Koro {s}ka cesta 160, Maribor 2000, Slovenia
Abstract
The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some results related to Posner's theorem as well as to Mayne's theorem are proved.