Proper Morphism

[Tsakanikas Nickos]

Let \( \displaystyle B = \bigoplus_{d \in \mathbb{N}} B_{d} \) be a graded ring generated by \( B_{1} \) as a \( B_{0} \)-algebra and suppose that \( B_{1} \) is a finitely generated \( B_{0} \)-module. Show that \( Proj(B) \longrightarrow Spec(B_{0}) \) is a proper morphism.