Over a Noetherian ring, every injective module is the direct sum of (uniquely determined) indecomposable injective modules. Over a commutative Noetherian ring, this gives a particularly nice understanding of all injective modules, described in . The indecomposable injective modules are the injective hulls of the modules "R"/"p" for "p" a prime ideal of the ring "R". Moreover, the injective hull "M" of "R"/"p" has an increasing filtration by modules "M""n" given by the annihilators of the ideals "p""n", and "M""n"+1/"M""n" is isomorphic as finite-dimensional vector space over the quotient field "k"("p") of "R"/"p" to Hom"R"/"p"("p""n"/"p""n"+1, "k"("p")).