Exercise 25, § 4

Let $A = \bigoplus_{n \geq 0} A_n$ be a Noetherian graded ring with positive degrees. Show that, if $A$ is a factorial domain, then $A_n$ is a factorial domain and the $A_n$ are reflexive. (To show that $A_0$ is a factorial domain, use criterion (c) of § 3, no. 2, Theorem 1; to show that the $A_n$ are reflexive, use Exercise 24.)