Products of commutators in matrix rings

Matej Brešar, Eusebio Gardella, Hannes Thiel

Let $R$ be a ring and let $n\ge 2$. We discuss the question of whether every element in the matrix ring $M_n(R)$ is a product of (additive) commutators $[x,y]=xy-yx$, for $x,y\in M…