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feat(RingTheory): is localization iff is localization on saturation#31135

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kckennylau:islocalization-saturation
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feat(RingTheory): is localization iff is localization on saturation#31135
kckennylau wants to merge 7 commits intoleanprover-community:masterfrom
kckennylau:islocalization-saturation

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@kckennylau kckennylau commented Oct 31, 2025 •
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In this PR we show that A is a localization of R on the submonoid S iff it is so on the saturation of S.
Crucially, the saturation of S is precisely the elements that become a unit in A.

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kckennylau added a commit to kckennylau/mathlib4 that referenced this pull request Oct 31, 2025
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sync with leanprover-community#31135
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github-actions bot commented Oct 31, 2025 •
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PR summary 286b90f429

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.RingTheory.Localization.Saturation (new file) 899

Declarations diff

+ ext_saturation
+ isLocalization_iff_of_saturation_eq
+ mem_saturation_iff_isUnit_algebraMap
+ of_saturation_eq
+ saturation_iff

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).

@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Oct 31, 2025
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mathlib4-merge-conflict-bot commented Nov 19, 2025

This pull request has conflicts, please merge master and resolve them.

@mathlib4-merge-conflict-bot mathlib4-merge-conflict-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Nov 19, 2025
@kckennylau kckennylau mentioned this pull request Nov 28, 2025
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@joneugster joneugster added the t-ring-theory Ring theory label Jan 31, 2026
@mathlib-dependent-issues mathlib-dependent-issues bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 3, 2026
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mathlib-dependent-issues bot commented Mar 3, 2026

This PR/issue depends on:

@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Mar 5, 2026
chrisflav
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@chrisflav chrisflav added the awaiting-author A reviewer has asked the author a question or requested changes. label Mar 5, 2026
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Thanks!
maintainer merge

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github-actions bot commented Mar 5, 2026

🚀 Pull request has been placed on the maintainer queue by chrisflav.

@mathlib-triage mathlib-triage bot added the maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. label Mar 5, 2026
@chrisflav chrisflav removed awaiting-author A reviewer has asked the author a question or requested changes. maintainer-merge A reviewer has approved the changed; awaiting maintainer approval. labels Mar 5, 2026
@mathlib-triage mathlib-triage bot assigned chrisflav and unassigned mattrobball Apr 2, 2026
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