A variation of supplemented modules

Over a general ring, an R-module is w-supplemented if and only if amply w-supplemented. It is proved that over a local Dedekind domain, all modules are w-supplemented and over a non-local Dedekind domain, an R-module M is w-supplemented if and only if Soc(M)\ll M or M=S0 \oplus (\bigoplusi \in I K), where S0 is a torsion, semisimple submodule of M and K is the field of quotients of R.

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