\begin{definition}[Definition:Dimension of Module]
Let $R$ be a ring with unity.
Let $G$ be a free $R$-module which has a basis of $n$ elements.
Then $G$ is said to have a '''dimension of $n$''' or to be '''$n$-dimensional'''.
The dimension of a free $R$-module $G$ is denoted $\map {\dim_R} G$, or just $\map \dim G$.
\end{definition}