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

Table of contents
- Solution i

Solution

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} + \dots + a_{0} = 0

with all

a_{i} \in A

.

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