Exercise 3, § 3

Let $A$ be a graded ring of type $A$ (where $A$ is torsion-free) and $M$ a strongly Laskerian finitely generated graded $A$-module (§ 2, Exercise 28). Show that the submodules $Q(p) = Q(p, e_p(M))$ (where $p$ runs through $\operatorname{Ass}_f(M)$) defined in Exercise 4 of § 2 are graded submodules.