Abstract
Let R be an associative ring. In this paper, we give a positive answer to the question of M.P. Drazin, “whether has a unique core-quasi-nilpotent decomposition implies that it must be quasi-invertible”.
Acknowledgments
The authors are highly grateful to the referee for his/her valuable comments and suggestions which led to improvements of this paper. In particular, the main result in Section 3 is suggested to the authors by the referee.