Chang Lin FU,Xin Song YANG,Gua
Herstein generalized Jacobson's famous theorem on the commutativity of rings in 1955 as follows. Theorem A. if for every x, y ∈ R, there is a polynomial p(t) with integer coefficients, depending possibly on x and y, such that [x - x2p(x), y] = 0, then R is commutative. In this paper, we define a property Fk of the polynomial f(x1,X2,…, xn) and prove, on the bassing is property, a theorem on the commutativity of rings. Herstein's theorem is just the one case when n = 1 in our theorem.