• COMMUTATIVITY OF ALTERNATIVE LEFT s-UNITAL RINGS WITH x[x^n,y]=y^r [x,y^m ]y

Abstract

Let R be an alternative left s-unital ring. In this paper we show that if are fixed non-negative integers and an alternative ring with unity 1 satisfies the polynomial identity (i) for all in , then is nil and if is -torsion free, then .  Also we show that an alternative left s-unital ring satisfying the polynomial identity (i) is commutative.