Vol. 7, No. 6, 2014

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On commutators of matrices over unital rings

Michael Kaufman and Lillian Pasley

Vol. 7 (2014), No. 6, 769–772
Abstract

Let $R$ be a unital ring and let $X\in {M}_{n}\left(R\right)$ be any upper triangular matrix of trace zero. Then there exist matrices $A$ and $B$ in ${M}_{n}\left(R\right)$ such that $X=\left[A,B\right]$.

Keywords
trace, matrix algebra, unital ring
Primary: 15A54
Secondary: 16S50