International Journal of Mathematics and Mathematical Sciences 
Volume 2005 (2005), Issue 9, Pages 1387-1391
doi:10.1155/IJMMS.2005.1387

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

Abstract

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.