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
Department of Mathematics, Faculty of Education, University of Maribor, Koroška cesta 160, Maribor 2000, Slovenia
Received 31 May 2004; Revised 17 January 2005
Copyright © 2005 Joso Vukman. 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
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.