# Definition:Ordered Basis

## Definition

Let $R$ be a ring with unity.

Let $G$ be a free $R$-module.

An ordered basis of $G$ is a sequence $\left \langle {a_k} \right \rangle_{1 \mathop \le k \mathop \le n}$ of elements of $G$ such that $\left\{{a_1, \ldots, a_n}\right\}$ is a basis of $G$.