Products of commutators in matrix rings

Let R be a ring and let n 2. We discuss the question of whether every element in the matrix ring Mₙ (R) is a product of (additive) commutators x, y=xy-yx, for x, y Mₙ (R). An example showing that this does not always hold, even when R is commutative, is provided. If, however, R has Bass stable rank one, then under various additional conditions every element in Mₙ (R) is a product of three commutators. Further, if R is a division ring with infinite center, then every element in Mₙ (R) is a product of two commutators. If R is a field and a Mₙ (R), then every element in Mₙ (R) is a sum of elements of the form a, xa, y with x, y Mₙ (R) if and only if the degree of the minimal polynomial of a is greater than 2.