环上幂等矩阵线性组合的Drazin逆

The Drazin Inverse of the Linear Combinations of Two Idempotent Matricesover Rings

给出了环R上幂等矩阵P,Q满足不同条件:(1)PQP=0;(2)PQP=PQ;(3)PQ=QP;(4)PQP=P时P+aQ的Drazin逆的表达式,推广了一些已有的结论.

For two idempotent matrices P, Q over an arbitrary ring R, the Drazin inverses of the linear combinations P ＋ aQ are obtained under the following conditions： （1）PQP = 0; （2）PQP = PQ; （3）PQ = QP; （4）PQP = P, and extend some known results.