A <ring extension> $A\subseteq B$ is an <integral extension> when every $b\in B$ is an <integral element> over $A$: there is a <monic polynomial>
$$
b^d+a_{d-1}b^{d-1}+\cdots+a_0=0
$$
with all $a_i\in A$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 101 / 2 / a / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-101/2/a/i/solution