Commutativity of rings via Streb's classification (Q1275861)

The author presents several commutativity theorems for rings, the proofs of which use a well-known result of W. Streb asserting that a ring must be commutative if it has no factor subrings of certain types. The principal theorem states that a ring \(R\) must be commutative if for each \(x,y\in R\) there exist integers \(m>0\) and \(n\geq 0\), and \(f(X),g(X),h(X)\in X^2\mathbb{Z}[X]\) with \(f(1)=\pm 1\), such that \([x,yx^m-x^nf(y)]=0\) and \([x-g(x),y-h(y)]=0\).