A Note on Constants of Integral Derivations in Semiprime Rings

Let R be a semiprime ring with extended centroid C and with Q its Martindale symmetric ring of quotients. Suppose that δ: R → R is a C-integral derivation. For a subring A of Q, let A(δ) denote the subring of constants of δ in A. We prove that R(δ) and Q(δ) satisfy the same polynomial identities with coefficients in C. In particular, R(δ) is not nil of bounded index.