Definition:Free Module on Set/Canonical Mapping

Definition
Let $R$ be a ring with unity.

Let $I$ be a set.

Let $R^{(I)}$ be the free $R$-module on $I$.

The canonical mapping $I \to R^{(I)}$ is the mapping that sends $i \in I$ to the $i$th standard basis element $e_i$.

Also see

 * Definition:Standard Basis of Free Module on Set