Exercise 27, § 1

Commutative Algebra, IX, p. 50

Let $r_1, r_2, n$ be integers satisfying

1 \leqslant r_1 \leqslant r_2 \leqslant n .

Let

T_1, ..., T_n

be indeterminates. By arguments analogous to those of the preceding exercise, give a description of the ring of Witt vectors over the ring

k[T_1, ..., T_{r_1}, T_1^{-1}, ..., T_{r_1}^{-1}, T_{r_1+1}, ..., T_{r_2}] [[T_{r_2+1}, ..., T_n]] .

Solution

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