International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 267-272
doi:10.1155/S0161171286000327
Certain near-rings are rings, II
Department of Mathematics, Brock University, St. Catharines L2S 3A1, Ontario, Canada
Received 20 August 1984
Copyright © 1986 Howard E. Bell. 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
We investigate distributively-generated near-rings R which satisfy one of the following conditions: (i) for each x,y∈R, there exist positive integers m, n for which xy=ymxn; (ii) for each x,y∈R, there exists a positive integer n such that xy=(yx)n. Under appropriate additional hypotheses, we prove that R must be a commutative ring.