The following theorem is proved: Let 1$"> r = r ( y ) > 1 , s , and t be non-negative integers. If R is a left s -unital ring satisfies the polynomial identity [ x y − x s y r x t , x ] = 0 for every x , y ∈ R , then R is commutative. The commutativity of a right s -unital ring satisfying the polynomial identity [ x y − y r x t , x ] = 0 for all x , y ∈ R , is also proved.