Definition:Ordered Basis

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

An ordered basis of $$G$$ is a sequence $$\left \langle {a_n} \right \rangle$$ of elements of $$G$$ such that $$\left\{{a_1, \ldots, a_n}\right\}$$ is a basis of $$G$$.