International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 87-92
doi:10.1155/S0161171296000130
Generalized periodic rings
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.
Abstract
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 x∈R\(N⋃C), there exist distinct positive integers m, n of opposite parity such that xn−xm∈N⋂C. 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.