Some commutativity results for S-unital rings

Abstract

In the present paper, it is shown that if R is a left ( resp. right) s-unital ring satisfying $[f(y^mx^ry^s) pm x^ty, x]$ = 0 (resp. $[f(y^mx^ry^s) pm yx^t, x]$ = 0), where m, r, s, t are fixed non-negative integers and $f(lambda)$ is a polynomial in $lambda^2{bf Z}[lambda]$, then R is commutative. Commutativity of R has also been investigated under different sets of constraints on integral exponents.