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  • Let denote the family of modules that are direct sums of some countably generated submodules . If is in , then each direct summand of is also in . (en)
  • If are countably generated modules with local endomorphism rings and if is a countably generated module that is a direct summand of , then is isomorphic to for some at most countable subset . (en)
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  • Lemma 1 (en)
  • Lemma 2 (en)
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  • Kaplansky's theorem on projective modules (en)
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