A commutativity theorem for left s-unital rings

Abstract

In this paper we generalize some well-known commutativity theorems for associative rings as follows: Let R be a left s-unital ring. If there exist nonnegative integers m>1, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative.