Let R be a prime ring without nonzero nil one-sided ideals. Suppose that g is a generalized derivation of R and that f(X 1 ,⋯,X k ) is a multilinear polynomial not central-valued on R such that g(f(x 1 ,⋯,x k )) is nilpotent for all x 1 ,⋯,x k in some nonzero ideal of R . Then g=0 .
關聯:
Taiwanese Journal of Mathematics, 10(5): 1183-1192
