Theorem 1

Let $A$ be a noetherian ring. For every injective $A$-module $I$, there exists one and only one family of cardinals $(a_{\mathfrak{p}})_{\mathfrak{p} \in \mathrm{Spec}(A)}$ such that $I$ is isomorphic to $\bigoplus_{\mathfrak{p}} I(\mathfrak{p})^{(a_{\mathfrak{p}})}$.