International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 87-92
doi:10.1155/S0161171296000130
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
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.