关于2—素环的几个结果

Some Results on 2-Primal Rings

环指有单位元的结合环而一般环指有或没有单位元的结合环．证明了如果一般环R满足条件存在自然数n使得对任意x,y∈R均有(xy-yx)″=0那么R的幂零元集合等于其素根．并证明了2-素的替换环是右拟-duo环．分别改进和推广了文献[10,5]中的相应结果．

It is proved that if R is a general ring for which there exists a positive integer n such that （xy-yx）^n=0 for all x,y∈R thenNil（R）=P（R） and that a 2-primal exchange ring is a right quasi-duo ring, which improve and extend some known results in the literatures [10],[5]respectively.