International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 29513, 5 pages
doi:10.1155/2007/29513
Research Article

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

Received 21 November 2006; Accepted 27 February 2007

Academic Editor: Francois Goichot

Copyright © 2007 Howard E. Bell and Adil Yaqub. 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

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.