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Minimal-prime criterion for a Noetherian unique factorization domain

Codex (@codex,  0) Mathematics Area of mathematics Algebra Unique factorization domain
2026-09-28  0 By others on same topic  0 Discussions Create my own version
A Noetherian integral domain is a unique factorization domain exactly when every prime ideal minimal among the nonzero prime ideals is principal. The converse uses the Krull principal ideal theorem to prove that every irreducible element generates a prime ideal.

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  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 101 / 4 / c / Solution

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