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“School of Mathematics”

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Paper   IPM / M / 12035
School of Mathematics
  Title:   Sums and products of square-zero matrices
  Author(s):  Ali Mohammadian
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  40
  Year:  2012
  Pages:   4568-4574
  Supported by:  IPM
  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.

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