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

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Solution

A minimal primary decomposition is an expression

I = Q_{1} \cap \dots \cap Q_{s}

in which every

Q_{i}

is a primary ideal, the prime ideals

Q_{i}

are pairwise distinct, and the decomposition is irredundant: deleting any

Q_{i}

changes the intersection.

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