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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 267-272
http://dx.doi.org/10.1155/S0161171286000327

Certain near-rings are rings, II

Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada

Received 20 August 1984

Copyright © 1986 Hindawi Publishing Corporation. 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,yR, there exist positive integers m, n for which xy=ymxn; (ii) for each x,yR, there exists a positive integer n such that xy=(yx)n. Under appropriate additional hypotheses, we prove that R must be a commutative ring.