Abstract: Let R be a ring. An R -module X is called c -injective if, for every closed submodule L of every R -module M , every homomorphism from L to X lifts to M . It is proved that if R is a Dedekind domain then an R -module X is c -injective if and only if X is isomorphic to a direct product of homogeneous semisimple R -modules and injective R -modules. It is also proved that a commutative Noetherian domain R is Dedekind if and only if every simple R -module is c -injective.