Commutativity theorems for s-unital rings with constraints on commutators

Abstract

Let R be an associative s-unital ring with the polynomial identity \( y^{s}[x^{n},y]=\pm [x,y^{m}]x^t\) or \( y^{s}[x^{n},y]=\pm x^{t}[x,y^{m}]\), where m, n, s and t are given non-negative integers such that m > 0 or n > 0 and m ≠ n if s = m − 1 and t = n − 1. Using similar methods as in our recent papers [1] and [2], we prove here the commutativity of R for various values of m, n, s and t, under appropriate constraints on torsion of commutators.