Abstract
Part of the recent work on near-rings has been concerned with sufficient conditions for near-rings to be commutative. Recently Howard E. Bell proved that if a d.g. near-ring R has an identity and for each x, y in R, there exists an n(x, y) > 1, such that (xy−yx)n(x, y) = xy − yx, then R is a commutative ring. In this paper we drop the requirement that R has an identity and show that the other condition is sufficient (and necessary) for R to be commutative. The inspiration for an important lemma, comes from a result of B.H. Neumann.
Publisher
Cambridge University Press (CUP)
Reference13 articles.
1. On the commutativity of near rings, II;Ligh;Kyungpook Math. J.,1971
2. Zero divisors and finite near-rings
3. The near-rings on groups of low order
4. Near-rings with descending chain condition;Ligh;Compositio Math.,1969
5. On the commutativity of near rings;Ligh;Kyungpook Math. J.,1970
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. References;Near Rings, Fuzzy Ideals, and Graph Theory;2013-05-21
2. IFP near-rings;Journal of the Australian Mathematical Society;1979-05
3. Bibliography;Near-Rings - The Theory and its Applications;1977
4. Some commutativity theorems for rings and near rings;Acta Mathematica Academiae Scientiarum Hungaricae;1976-03
5. A special class of near rings;Journal of the Australian Mathematical Society;1974-12