Exercise 6, § 1

Let A be a $\mathbf{Z}_{(p)}$-algebra. Let $n$ be an integer, $n \geqslant 1$, $g = (g_0, ..., g_{n-1})$ an element of $W_n(A)$, and let $f = g_0$. Then, denoting by $A_f$ (resp. $W_n(A)_g$) the localization of A (resp. $W_n(A)$) with respect to the multiplicative system of powers of $f$ (resp. $g$), one has $W_n(A_f) = W_n(A)_g$.