环上的强-Drazin逆

On Strongly Drazin Inverses in a Ring

环R中的元素a有强-Drazin逆,如果环R中的元素x满足x^2a=x,ax=xa,a-ax∈N(R).x是唯一的,并且被称为元素a的强-Drazin逆.文章推广了Cline公式到强-Drazin逆的情形,并给出了在多项式条件a^2b=aba且b^2a=bab下强-Drazin逆的一些加性结果,从而将Drazin逆的相应结论推广到了强-Drazin逆上.

An element a∈R has strongly Drazin inverse in case there is an element x∈R satisfying x^2a=x,ax=xa,a-ax∈N(R).Here x is unique,and is called a strong Drazin inverse of a∈R.This paper generalize Cline's formula to the case of the strongly Drazin inverse,obtains some additive results for the strongly Drazin inverse under the polynomial conditions a^2b=aba and b^2a=bab,and extends the corresponding results for Drazin inverses to strongly Drazin inverses.