# Definition:Basis of Vector Space/Definition 1

## Definition

Let $R$ be a division ring.

Let $\struct {G, +_G, \circ}_R$ be an vector space over $R$.

A basis of $G$ is a linearly independent subset of $G$ which is a generator for $G$.

## Linguistic Note

The plural of basis is bases.

This is properly pronounced bay-seez, not bay-siz.