Definition:Coordinate System

Definition
Let $R$ be a ring with unity.

Let $\left \langle {a_k} \right \rangle_{1 \mathop \le k \mathop \le n}$ be an ordered basis of a free $R$-module $G$.

Then $\left \langle {a_k} \right \rangle_{1 \mathop \le k \mathop \le n}$ can be referred to as a coordinate system.