A variation of supplemented modules
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Date
2013
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Abstract
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) << M or M = $S_0$ &#8853; ($&#8853;_{i&#8712;I}$ K), where $S_0$ is a torsion, semisimple submodule of M and K is the field of quotients of R.