Let $R$ be a ring with identity, let $M$ be a left $R$-module, and let $(e_i)_{i \in I}$ be a basis of $M$. Let $\bigoplus_{i \in I} R$ denote the left $R$-module of finitely supported families $(r_i)_{i \in I}$ with $r_i \in R$, equipped with coordinatewise addition and scalar multiplication. Define the map
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\begin{align*}
\Phi: \bigoplus_{i \in I} R \to M
\end{align*}