International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 26, Pages 1393-1396
On the mapping in an
1Department of Mathematics and Computer Science, Nicholls State University, Thibodaux 70310, LA, USA
2Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504, LA, USA
Received 26 August 2002
Copyright © 2004 Scott J. Beslin and Awad Iskander. 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.
We consider the following condition (*) on an associative ring
. There exists a function from into such that is a group homomorphism of , is
injective on , and for some
positive integer . Commutativity and structure are
established for Artinian rings satisfying (*), and a
counterexample is given for non-Artinian rings. The results
generalize commutativity theorems found elsewhere. The case is examined in detail.