Let R be a semiprime ring and C the center of R. In this paper following results areobtained:1.Suppose for any x_1,…,x_n∈R, there exists a polynomial f(t_1,…,t_n)(f dependingon x_1,…,x_n) such that f(x_1,…,x_n)∈C. If these polynomials satisfy the bounded condition,the sums of some coefficients of each f prime to each other, then R is commutative, which isageneralization of all related results in[ 2-27]. If f ls a polynomial, the sum of coefficients satisfiessome conditions, and for any x_1,…,x_n∈R, there exists an integer m(x_1,…,x_n)> 1 such thatf(x_1,…,x_n)￣m(x_1,…,x_n)=f(x_1,…,x_n), then R is commutative.
