Reducts of (C, +, *) which Contain +

We show that the structure (C, +, •) has no proper non locally modular reducts which contain +. In other words, if X⊂C n is constructible and not definable in the module structure (C, +, λ a ) a∈C (where λ a denotes multiplication by a) then multiplication is definable in (C, +, X)