Definition:Dimension of Module

Definition
Let $G$ 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 (unitary) module is finite-dimensional if it is $n$-dimensional for some $n \in \N_{>0}$.

The dimension of a unitary $R$-module $G$ is denoted $\dim \left({G}\right)$.