Definition:Dimension (Linear Algebra)

Module
Let $$\left({G, +_G: \circ}\right)_R$$ be a unitary $R$-module which has a basis of $$n$$ elements.

Then $$G$$ is said to have a dimension of $$n$$ or to be $$n$$-dimensional.

A module is finite-dimensional if it is $$n$$-dimensional for some $$n \in \mathbb{N}^*$$.