Abstract
A derivation of an associative ring R is an additive map satisfying T(xy) = T(x)y + xT(y) for all x, y in R. We study rings with a derivation T satisfying Herstein's condition [T(R), T(R)] = 0. (The commutator [u, v] is defined by: [u, v] = uv - vu.) This work studies the structure of the ideal I generated by T(R). We show that I-3 is in the center of R, and we show that R has an ideal K which is contained in the kernel of T, K-2 = 0, and [T(R/K), R/K] generates a trivial ideal of R/K.