Corollary 1

If E is a torsion-free A-module, the canonical mapping φ : E → E_{(K)} is injective.

Recall (§ 5, no. 1) that for every A-linear mapping of E into a vector space F over K, there exists one and only one K-linear mapping $\vec{f} : E_{(K)} \to F$ such that $f = \vec{f} \circ \phi$; we shall say that $\vec{f}$ is associated with $f$.