By a classical result, for any field F and a positive integer n, a matrix in Mn( F) is a commutator if only and if it has trace zero. This is no longer true if F is replaced with an arbitrary ring R. But the only known examples of matrices which have trace zero and are not commutators are of the size 2 x 2. The purpose of this thesis is to construct an n x n matrix for any positive integer n ≥ 2 which has trace zero but is not a commutator.
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