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Module
Definition
$M,R$ |
$\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{module}(\mathcal M,\mathcal R)$ |
$\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(\mathcal M,\mathcal R)$ |
$\mathcal M\in \mathrm{abelianGroup}(M)$ |
Now denote the multiplication in the ring $\mathcal R$ by “$\ \hat*\ $”.
$r,s\in R$ |
$r*s=s*r$ |
Discussion
A module is a left module with a commutative ring acting on the group.
One generally speaks of an $R$-module over $M$. Here $R$ and $M$ are just sets.
Reference
Wikipedia: Module