摘要 : Let R be an associative ring. An additive map F : R -> R is called a generalized derivation if there exists a derivation d of R such that F(xy) = F(x)y + xd(y) for all x, y is an element of R. In [7], Herstein proved the follow... 展开 Let R be an associative ring. An additive map F : R -> R is called a generalized derivation if there exists a derivation d of R such that F(xy) = F(x)y + xd(y) for all x, y is an element of R. In [7], Herstein proved the following result: If R is a prime ring of char(R) not equal 2 admitting a nonzero derivation d such that [d(x), d(y)] = 0 for all x, y is an element of R, then R is commutative. In the present paper, we shall study the above mentioned result for generalized derivations in rings with involution. 收起