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ClueBot NG (talk | contribs) m Reverting possible vandalism by 2604:3D09:797D:3500:68F6:3062:AD4:F3DF to version by David Eppstein. Report False Positive? Thanks, ClueBot NG. (4239131) (Bot) |
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=== Formal definition ===
Suppose that ''R'' is a [[Ring (mathematics)|ring]], and 1 is its multiplicative identity.
A '''left ''R''-module''' ''M'' consists of an [[abelian group]] {{nowrap|(''M'', +)}} and an operation {{nowrap|'''·''' : ''R'' × ''M'' → ''M''}} such that for all ''r'', ''s'' in ''R'' and ''x'', ''y'' in ''M'', we have
#<math> r \cdot ( x + y ) = r \cdot x + r \cdot y </math>
#<math> ( r + s ) \cdot x = r \cdot x + s \cdot x </math>
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