关于半质环的几个交换性条件

Some commutativity conditions for semi-prime rings

设R为结合环,Z(R)为其中心。证明了:设R为半质环,a∈R,2a为非零因子,正整数n=n(x,y)及M,其中1<n=n(x,y)≤M.如果x,y∈R有依赖于x,y的多项式fxy(X,Y)∈A[X,Y]使得[fxy(x,a),yn]∈Z(R),则R为交换环。推广了文献[1-4]中的结果,得到更广泛的交换性条件。

Suppose R is an associative ring,Z（R） is its center. It is shown that： Suppose R is a semi -prime ring,α∈R, and 2α is not zero -divisor, n =n（x,y） and M are positive integers with 1 〈n =n（x,y） ≤M. If for everyx,y E R, there is a polynomialfxy（ X, Y） ∈ A [X, Y] such that Efxy （x, α） ,yn] ∈Z（R）, then R is called a commuta- tive ring. The results of documents [ 1 - 4] are extended and more extensive commutativity conditions of the semi - prime ring are obtained.