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Put in another way, there is a surjection
: <math> \bigoplus_{g \in G} R \to M, \, r_g \
where we wrote ''r''<sub>''g''</sub> for an element in the ''g''-th component of the direct sum. (Coincidentally, since a generating set always exists; for example, ''M'' itself, this shows that a module is a quotient of a free module, a useful fact.)
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