\begin{definition}[Definition:Coordinate System]
Let $R$ be a ring with unity.
Let $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$ be an ordered basis of a free $R$-module $G$.
Then $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$ can be referred to as a '''coordinate system'''.
\end{definition}