Cline's Formula for the Generalized Drazin Inverse
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1
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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.
Classification :
15A09, 16S10
@article{BMMS_2014_37_1_a2,
author = {Yihua Liao and Jianlong Chen and Jian Cui},
title = {Cline's {Formula} for the {Generalized} {Drazin} {Inverse}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2014},
volume = {37},
number = {1},
url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a2/}
}
Yihua Liao; Jianlong Chen; Jian Cui. Cline's Formula for the Generalized Drazin Inverse. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a2/