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Abstract
Let C ∈ F n×n have minimum polynomial m(x). Suppose C is of zero trace and m(x) splits over F. Then, except when n = 2 and m(x) = (x − c)2 or when n = 3 and m(x) = x − c)2 with c ≠ 0, there exist nilpotents A, B ∈ F n×n such that C = AB − BA.