Abstract. A semiderivation of a ring R is an additive mapping / : R -• R together with a function g : R -• R such that f(xy) = f{x)g(y) + xf(y) = f(x)y + g(x)f(y) andIf / is a non-zero semiderivation of a prime ring R, then it is well known that g must necessarily be an endomorphism. Let R be a prime ring with center Z(R), f a non-zero semiderivation with associated endomorphism g which is one-one & onto, and a, r be two automorphisms of R such that fa = erf, fr = rf, go = ag, gr = rg. Suppose that U is a non-zero (cr, r)-Lie ideal of R and C(R)a,T = {c G R \ ca(x) = T(X)C,for all x € R}. In the present paper it is shown that (i) if char R IntroductionLet R be a ring with center Z(R), and U an additive subgroup of R.