Solution (source code)

= Solution

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.