Exercise 1, § 4

Let $\mathbf{A}$ be an integrally closed Noetherian domain, and $V$ a vector space of finite rank over the field of fractions of $A$. Show that, if $(M_\lambda)$ is any family of reflexive lattices of $V$ all containing the same lattice $N$, the lattice $M = \bigcap_\lambda M_\lambda$ is reflexive (consider the dual lattices $M_\lambda^*$).