【摘要】 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。更多还原

【Abstract】 Suppose R is an associative ring,Z(R) is its center. It is shown that: Suppose R is a semi-prime ring, a∈R, and 2a is not zero-divisor, n=n(x,y) and M are positive integers with 1<n=n(x,y)≤M. If for every x,y∈R, there is a polynomial fxy(X,Y)∈A[X,Y]such that [fxy(x,a),yn]∈Z(R), then R is called a commutative ring. The results of documents [1-4] are extended and more extensive commutativity conditions of the semi-prime ring are obtained.更多还原