Volume 37 • Number 1 • 2014   • Cline's Formula for the Generalized Drazin Inverse Yihua Liao, Jianlong Chen and Jian Cui Abstract. It is well known that for an associative ring $R$, if $ab$ is Drazin invertible then $ba$ is Drazin invertible. In this case, $(ba)^D=b((ab)^D)^2a.$This formula is so-called Cline's formula. In this note, we generalize Cline's formula to the case of the generalized Drazin invertibility. 2010 Mathematics Subject Classification: 15A09, 16S10 Full text: PDF