\begin{definition}[Definition:Ordered Basis]
Let $R$ be a ring with unity.
Let $G$ be a free $R$-module.
An '''ordered basis''' of $G$ is a sequence $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$ of elements of $G$ such that $\set {a_1, \ldots, a_n}$ is a basis of $G$.
\end{definition}