Injectivity relative to closed submodules over Krull domains

Assume that R is an associative ring with identity. An R-module X is called c-injective if, for every closed submodule K of every R-module M, every homomorphism from K to X extends to M. In this paper, we show that a strong Mori domain D is a Krull domain if and only if every w-simple D-module is c-injective. As a result, over a Krull domain, if M is a direct product of w-simple modules, then any homomorphism from a closed submodule K of M to M can be lifted to M.