This is an old revision of the document!
Vector space
Definition
$V,F$ |
$\langle\mathcal V,\mathcal F, *\rangle \in \mathrm{vectorSpace}(V,F)$ |
$\langle\mathcal V,\mathcal F, *\rangle \in \mathrm{module}(V,F)$ |
$\mathcal F\in \mathrm{field}(F)$ |
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