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feat(RingTheory): UFD criteria via height 1 prime ideals and localization#36739

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mbkybky wants to merge 17 commits intoleanprover-community:masterfrom
mbkybky:ufd_lemmas
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feat(RingTheory): UFD criteria via height 1 prime ideals and localization#36739
mbkybky wants to merge 17 commits intoleanprover-community:masterfrom
mbkybky:ufd_lemmas

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@mbkybky
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@mbkybky mbkybky commented Mar 16, 2026

We prove the following UFD criteria via height 1 prime ideals and localization:

  1. Let R be a Noetherian domain. Then R is a UFD if and only if every height 1 prime ideal is principal.
  2. Let R be a Noetherian domain, x ∈ R be a prime element. If Rₓ is a UFD, then R is also a UFD.

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@github-actions github-actions bot added the t-ring-theory Ring theory label Mar 16, 2026
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github-actions bot commented Mar 16, 2026

PR summary 4ec5d95aa6

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.RingTheory.Ideal.UFD (new file) 1857

Declarations diff

+ Away.isDomain
+ Ideal.eq_span_singleton_of_primeHeight_eq_one
+ Ideal.isPrincipal_of_isPrincipal_localization_away_of_prime
+ Ideal.primeHeight_eq_zero_iff_eq_bot
+ Ideal.ufd_iff_height_one_primes_principal
+ ufd_of_ufd_localization_away_of_prime

You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

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tb65536 commented Mar 20, 2026

Note #36781

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3 participants