International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 87-92

Generalized periodic rings

Howard E. Bell1 and Adil Yaqub2

1Department of Mathematics, Brock University, St. Catharines, Ontario, Canada
2Department of Mathematics, University of California, Santa Barbara, CA, USA

Received 18 March 1994; Revised 13 March 1995

Copyright © 1996 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.


Let R be a ring, and let N and C denote the set of nilpotents and the center of R, respectively. R is called generalized periodic if for every xR\(NC), there exist distinct positive integers m, n of opposite parity such that xnxmNC. We prove that a generalized periodic ring always has the set N of nilpotents forming an ideal in R. We also consider some conditions which imply the commutativity of a generalized periodic ring.