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Math Help - free R-module, subset basis

  1. #1
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    free R-module, subset basis

    Let R be a ring and M a free R-module. Prove that a subset S \subseteq M is a basis for M if and only if every m \in M may be expressed uniquely as a linear combination of elements of S.
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  2. #2
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    S generates M <=> existence

    S is free <=> unicity
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