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Gnampfissimo (talk | contribs) m →Multiplicative set: Typo fixed |
→Localization of a module: editted the definition of scalar multiplication of $S^{-1}R$-module $S^{-1}M$. |
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Addition and scalar multiplication are defined as for usual fractions (in the following formula, <math>r\in R,</math> <math>s,t\in S,</math> and <math>m,n\in M</math>):
:<math>\frac{m}{s} + \frac{n}{t} = \frac{tm+sn}{st},</math>
:<math>\frac rs \frac{m}{
Moreover, {{math|''S''<sup>−1</sup>''M''}} is also an {{mvar|R}}-module with scalar multiplication
:<math> r\, \frac{m}{s} = \frac r1 \frac ms = \frac{rm}s.</math>
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