A <minimal primary decomposition> is an expression
$$
I=Q_1\cap\cdots\cap Q_s
$$
in which every $Q_i$ is a <primary ideal>, the prime ideals $\sqrt{Q_i}$ are pairwise distinct, and the decomposition is irredundant: deleting any $Q_i$ changes the intersection.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 101 / 2 / a / Solution

A minimal primary decomposition of an ideal $I$ is an irredundant finite intersection $I=\bigcap_iQ_i$ of primary ideals whose radicals are pairwise distinct.


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