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

TakeThenEvery prime ideal in the image ofis 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.