广义n-强Drazin逆的注记

首先, 在条件acd=dbd, bdb=bac下给出广义n-强Drazin可逆元的Cline公式及Jacobson引理; 其次, 给出广义n-强Drazin可逆的幂等元相等的等价刻画; 最后, 在条件acd=dbd, dba=aca下讨论广义n-强Drazin可逆元相似的等价刻画以及多元素相似性问题.

Notes on Generalized n-Strong Drazin Inverse

Firstly, the Cline’s formula and Jacobson’s lemma for generalized n-strong Drazin inverse were given under the conditions of acd=dbd, bdb=bac. Secondly, the equivalent characterizations of generalized n-strong Drazin inverse idempotent elements equality were given. Finally, the equivalent characterizations of generalized n-strong Drazin invertible element similarity and the problem of multi-element similarity under the condition of acd=dbd, dba=aca were discussed.