幂零矩阵生成的幂零子代数

NILPOTENT SUB ALGEBRAS GENERATED BY NILPOTENT MATRICES

域F上的全矩阵代数M_n(F)的幂零矩阵a与b如果满足条件:对一切自然数s与t0≤s+t≤n,a^sb^t是幂零的且rank(a)=ind(a)-1,则a与b生成的子代数<a,b>是幂零的。

Suppose a and b are nilpotent matrices of M.(F) and for all a and 1: 0+t are nilpotent .The paper is proved that If rank ii - ind a-1 ,then the subalgebra(a,b)of M.(F) generated by a and b is nilpotent.