The assertion is false. The <integer>[integers] $\mathbb Z$ form a <Noetherian ring>, since every <ideal> is <principal ideal>[principal], but this ring is not an <Artinian ring>: the strictly descending chain
$$
(2)\supsetneq(2^2)\supsetneq(2^3)\supsetneq\cdots
$$
never stabilizes.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 101 / 1 / a / i / Solution

 Solution

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