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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 101

Put $g=y^2-zw$. Every generator of $I$ is divisible by $x^2$ and belongs to $(y,z)^2$, while the displayed decomposition in the next part will show that
$$
\sqrt I=(x)\cap(y,z).
$$
Its two minimal primes, and hence its isolated associated primes, are
$$
\boxed{\mathfrak p_1=(x),
\qquad \mathfrak p_2=(y,z).}
$$
The corresponding isolated primary components are
$$
\boxed{\mathfrak q_1=(x^2),
\qquad \mathfrak q_2=(y,z)^2=(y^2,yz,z^2).}
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 101 / 5 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 101 / 5 / a / Solution

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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 101 / 5 / a / Solution

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