Exercise 6, § 6

Let $A$ be a Grothendieck ring, $I$ an ideal of $A$, and $\widehat{A}$ the separated completion of $A$ for the $I$-adic topology. Prove that $\widehat{A}$ is an A-algebra absolutely regular. (Let $\mathfrak{n}$ be a maximal ideal of $\widehat{A}$, and m its inverse image in A; deduce from Exercise 3 that $\widehat{A}_\mathfrak{n}$ is an $A_m$-algebra absolutely regular.)