拟环成为结合环的条件

本文给出D—拟环成为结合环的几个条件，推广了Bell和Ligh等人的结果．

Some Conditions for Near-rings to Be Rings

In this paper,the following theorems are proved:Theorem1 Let N be a semiprime D - nr,if N satisfies one of the following conditions,then N is a commutativering.(1) for each x,yN tilers exists an integer n(x,y)>1 such that,(xy)n(x,y)=xy.(2) for each x,yN there exists an integer n(x,y)>1 such that,(xy)n(x,y)=yx,(3) for each x,yN there exists an integer n(x,y)>1 such that (xy-yx)n(x,y)=xy-yxor(xy+yx)n(x,y)Theorem2 Let N be a D - nr and for each xN there exists an integer n(x)>1 such that xn(x)=xthe N is a commutative rings.