An iteration technique and commutativity of rings (Q917662)

Let R denote a ring with 1. The authors present several theorems asserting that R must be commutative if it satisfies a certain commutator identity and has a suitable restriction on torsion. For example, R is commutative if there exist integers m and n, each greater than 1, for which R is n!m!-torsion-free and satisfies the identity \([x^ my^ n- yx^ my,y]=0\). The results are unsurprizing extensions of earlier work of several other authors; the real point of the paper is to demonstrate the usefulness and efficiency of an iteration technique due to \textit{J. Tong} [Can. Math. Bull. 27, 456-460 (1984; Zbl 0545.16015)].