Commutativity theorems for rings with constraints on commutators (Q1187065)

Let \(R\) be a ring with 1 satisfying a polynomial identity of the form \(y^ s[x^ n,y]=[x,y^ m]x^ t\), where \(n\), \(m\), \(s\), and \(t\) are non-negative integers and \(n>1\). Under various additional hypotheses, it is proved that \(R\) is commutative. The results yield several earlier commutativity theorems as corollaries.