Corollary 2

Let $a$ be a right ideal of $A$, $F$ a left $A$-module and $aF$ the sub-$\mathbf{Z}$-module of $F$ generated by the elements of the form $\lambda x$, where $\lambda \in a$ and $x \in F$. Then there is a canonical $\mathbf{Z}$-module isomorphism

*such that, for all $\bar{\lambda} \in A/a$ and all $x \in F$, $\pi(\bar{\lambda} \otimes x)$ is the class mod. $aF$ of $\lambda x$, where $\lambda \in \bar{\lambda}$.

In particular, for $A = \mathbf{Z}$, it is seen that for every integer $n$ and every $\mathbf{Z}$-module $F$, $(\mathbf{Z}/n\mathbf{Z}) \otimes_{\mathbf{Z}} F$ is canonically identified with the quotient $\mathbf{Z}$-module $F/nF$.