Exercise 30, § 2

Let $K$ be an infinite commutative field and $A$ the ring of formal power series $K[[X, Y]]$ in two indeterminates, which is a complete Hausdorff Noetherian local ring. Define a multiplicative subset $S$ of $A$ such that $S^{-1}A$ is not a semi-local ring (if $(\lambda_n)$ is an infinite sequence of distinct elements of $K$, consider the prime ideals $p_n = A(X + \lambda_n Y)$ of $A$).