## Module

### Set

 context $M,R$ postulate $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{module}(\mathcal M,\mathcal R)$ context $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(\mathcal M,\mathcal R)$ context $\mathcal M\in \mathrm{abelianGroup}(M)$

Now denote the multiplication in the ring $\mathcal R$ by “$\ \hat*\$”.

 $r,s\in R$
 postulate $r*s=s*r$

### 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