Module Theory: Isomorphism

Let $$R$$ be a PID and consider the ideals $$(a),(c),(ac) \subset R$$. Consider R/(ac) and R/(a) x R/(c).

Is there a natural surjective homomorphism from one of these modules to the other?

• Maps into a product are equivalent to pairs of maps into the factors. For modules, maps from a direct sum (equivalently, direct product when only finitely many factors) are equivalent to maps from each summand/factors. – Arturo Magidin Nov 23 at 1:33