Exercise 35, § 2

Let K be a commutative field, B the valuation ring, whose group of orders is R, formed by the “formal series” $\sum_{x} c_x T^x$ where $c_x \in K$, $x \in \mathbf{R}_+$ and the set of x such that $c_x \neq 0$ is well ordered; the ring A defined in § 1, Exercise 2 is a subring of B and B is a flat A-module. If C is the A-module defined in § 1, Exercise 2, now prove that one has $\operatorname{Ass}_B(C \otimes_A B) \neq \varnothing$ though $\operatorname{Ass}_A(C) = \varnothing$ (consider an element of $C \otimes_A B = B/\mathfrak{a}B$, canonical image of an element of B of valuation α).*