Exercise 35, § 2

Let $K$ be a commutative field, $B$ the valuation ring, whose order group is $\mathbf{R}$, consisting of the "formal power 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, show that $\operatorname{Ass}_B(C \otimes_A B) \neq \varnothing$ although $\operatorname{Ass}_A(C) = \varnothing$ (consider an element of $C \otimes_A B = B/aB$ the canonical image of an element of $B$ of valuation $a$). \*