International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1387-1391

A weak periodicity condition for rings

Hazar Abu-Khuzam,1 Howard E. Bell,2 and Adil Yaqub3

1Department of Mathematics, American University of Beirut, Beirut 1107 2020, Lebanon
2Department of Mathematics, Brock University, ON, St. Catharines L2S 3A1, Canada
3Department of Mathematics, University of California, Santa Barbara 93106, CA, USA

Received 24 February 2005

Copyright © 2005 Hazar Abu-Khuzam et al. 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.


A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson radical can be written as the sum of a potent element and a nilpotent element. After discussing some basic properties of such rings, we investigate their commutativity behavior.