Certain near-rings are rings, II - Howard E. Bell (International Journal of Mathematics and Mathematical Sciences)
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.