A Generalization of a Jacobsons Commutativity Theoram

In this paper we study the structure and the commutativity of a ring R, in which for each x,y ∈ R, there exist two integers depending on x,y such that [x,y]1,>≥nkok equals x n or y n.In this paper we study the structure and the commutativity of a ring R, in which for each x,y ∈ R, there exist two integers depending on x,y such that [x,y]1,>≥nkok equals x n or y n.