Exercise 16, § 1

Let B be a ring, A a subring of B and f the ideal of A the annihilator of the A-module B/A. Let U be the complement in X = Spec(A) of the closed set V(f) and let u = ^a ρ, where ρ : A → B is the canonical injection. Show that the restriction of u to ^{-1}u(U) is a homeomorphism of ^{-1}u(U) onto U (foreveryelement g ∈ f, consider the spectrum of the ring A, identified with the open set X, ⊂ U).