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

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.