===== Module =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $M,R$ |
| @#55EE55: postulate   | @#55EE55: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{module}(\mathcal M,\mathcal R)$ |
| @#55CCEE: context     | @#55CCEE: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(\mathcal M,\mathcal R)$ |
| @#55CCEE: context     | @#55CCEE: $\mathcal M\in \mathrm{abelianGroup}(M)$ |

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

| $r,s\in R$ |

| @#55EE55: postulate   | @#55EE55: $r*s=s*r$ |

==== 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: [[http://en.wikipedia.org/wiki/Module_%28mathematics%29|Module]]
==== Parents ====
=== Subset of ===
[[Left module]]