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Explicitly, if ''G'' is a generating set of a module ''M'', then every element of ''M'' is a (finite) ''R''-linear combination of some elements of ''G''; i.e., for each ''x'' in ''M'', there are ''r''<sub>1</sub>, ..., ''r''<sub>''m''</sub> in ''R'' and ''g''<sub>1</sub>, ..., ''g''<sub>''m''</sub> in ''G'' such that
: <math> x = r_1 g_1 + \cdots + r_m g_m.
Put in another way, there is a surjection
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