Let $R$ be a unital ring, let $M$ be a left $R$-module, and let $B = \{b_1,\ldots,b_n\}$ be a finite module basis of $M$, with the displayed ordering fixed; equivalently, $B$ spans $M$ over $R$ and is linearly independent over $R$. Define the map $\varphi: R^n \to M$ by