补右零化子与环的交换性定理

Complementary right annihilators and commutativity theorems of rings

设R是一个有单位元的结合环,I是R的补右零化子集,且n为正整数,若对任意x∈R\I,y∈R,有(xy)^(n+k)=x^(n+k)y^(n+k),k=0,1,2,则R是交换环.

Let Rbe an associative ring with identity.I be a complementary right annihilator of R.It is shown that if for any x∈R／I,y∈R,（xy）^（n＋k）=x^（n＋k）y^（n＋k）,k=0,1,2,where nis a fixed positive integer,then Ris a commutative ring.