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.

https://www.youtube.com/watch?v=yZ2dO6Fy5Kc

Reference

Wikipedia: Module

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