===== Vector space =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $V,F$ |
| @#FFBB00: definiendum | @#FFBB00: $\langle\mathcal V,\mathcal F, *\rangle \in \mathrm{vectorSpace}(V,F)$ |
| @#55CCEE: context     | @#55CCEE: $\langle\mathcal V,\mathcal F, *\rangle \in \mathrm{module}(V,F)$ |
| @#55CCEE: context     | @#55CCEE: $\mathcal F\in \mathrm{field}(F)$ |

==== 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: [[http://en.wikipedia.org/wiki/Vector_space|Vector space]]
==== Parents ====
=== Subset of ===
[[Module]]
=== Context ===
[[Field]]