Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 101 / 4 / ii / a

Table of contents
- Solution a

Solution

Take

f = T_{1} T_{2} - 1.

Then

A = R [T_{1}, T_{2}] / (T_{1} T_{2} - 1) ≅ R [t_{1}, t_{1}^{- 1}] .

Every prime ideal in the image of

Spec A ⟶ Spec R [t_{1}]

is disjoint from the multiplicative set

{1, t_{1}, t_{1}^{2}, \dots}

. In particular, the prime ideal

(t_{1})

is not in the image, so the contraction map is not surjective.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version