Commutativity of rings with variable constraints

Abstract

Let m > 1, r ≥ 0 be fixed non-negative integers and R a ring with unity 1 in which for each x ∈ R, there exists a polynomial f (X,The main result of the present paper asserts that R is commutative if it satisfies the property Q(m) (for all x, y ∈ R, m[x, y] = 0 implies [x, y] = 0). Finally, some results have been extended to one-sided s-unital rings.