Free groupLet $A$ be an abelian group. Let $(e_i)_{i \in I}$ be a family of elements of $A$. We say that this family is a basis for $A$ if the family is not empty, and if every element of $A$ has a unique expression as a linear expression x = \sum_{i \in I} x_i e_iwhere $x_i \in \mathbb{Z}$ and almo……