Exercise 30, § 2

Let $K$ be an infinite commutative field, $A$ the ring of formal power series $K[[X, Y]]$ in two indeterminates, which is a separated complete 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).