## Vector space

### Set

 context $V,F$ definiendum $\langle\mathcal V,\mathcal F, *\rangle \in \mathrm{vectorSpace}(V,F)$ context $\langle\mathcal V,\mathcal F, *\rangle \in \mathrm{module}(V,F)$ context $\mathcal F\in \mathrm{field}(F)$

### Ramifications

#### Discussion

A vector space is a $F$-module over $V$, where $F$ is a field, not just a ring.

One speaks of an $F$-vector space over $V$. Here $F$ and $V$ are just sets.

#### Reference

Wikipedia: Vector space