“School of Mathematics”
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| Paper IPM / M / 12035 |
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| Abstract: | |
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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.
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