International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 29513, 5 pages
doi:10.1155/2007/29513
On generalized periodic-like rings.
Howard E. Bell1
and Adil Yaqub2
1Department of Mathematics, Brock University, St. Catharines L2S 3A1, Ontario, Canada
2Department of Mathematics, University of California, Santa Barbara 93106, CA, USA
Abstract
Let R be a ring with center Z, Jacobson radical J, and set N of all nilpotent elements. Call R generalized periodic-like if for all x∈R∖(N∪J∪Z) there exist positive integers m, n of opposite parity for which xm−xn∈N∩Z. We identify some basic properties of such rings and prove some results on commutativity.