Let R be a C-algebra over a commutative ring C of zero characteristic. An element a ∈ R will be called separable if there exists p ∈ C[x] for which p(a) = 0 and such that p′(a) is invertible, where p′ is the formal derivative of p. Call A the C-algebra generated by aR and aL the right and left multiplications by a, and write Da for the inner derivation defined by a. It will be shown that when a is separable there exists φ ∈ A such that [p′(a)]−1φ Da is idempotent. As a consequence it follows that the additive group of R may be decomposed into a direct sum of Ker Da and Im Da. Another result is that for an arbitrary C-derivation δ there exists d ∈ Im Da such that aδ = aDd. Thus Ker Da (and also Im Da) is a δ-subgroup of R+ if and only if aδ = 0.