Abstract
We show that for any two n × n square-zero matrices A and B over a division ring, if the right column spaces of AB and BA are the same, then the rank of AB is at most n/4, and if, in addition, the right null spaces of AB and BA are the same, then the rank of A + B is at most n/2. This generalizes some known results.
ACKNOWLEDGMENTS
This research was in part supported by a grant from IPM (No. 91050405). The author is grateful to the anonymous referee for valuable comments.
Notes
Communicated by M. Cohen.