多重线性多项式上广义导子的幂零问题

Generalized Derivations with Nilpotent Values on Multilinear Polynomials

R是素环,g是R的非零广义导子,f(X1,…,Xt)是多重线性多项式,在R上不为零.如果g(f(x1,…,xt))n=0, x∈I,其中n是固定正整数,I是R的非零理想,那么f(X1,…,Xt)在R上是中心值的.

Let R be a prime ring,g be a nonzero generalized derivation of R,and f(X_1,…,X_t) a multilinear Polynomial not vanishing on R. Suppose that g(x_1,…,x_t)~n=0.for all x_1,…,x_t in some nonzero ideal I of R, where n is a fixed integer. Then f(X_1,…,X_t) is central-valued on R.