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[Merged by Bors] - feat(RingTheory/Radical): Theorems for coprime elements + alpha #15331

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@seewoo5 seewoo5 commented Jul 30, 2024

@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Jul 30, 2024
@seewoo5 seewoo5 added t-algebra Algebra (groups, rings, fields, etc) and removed new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! labels Jul 30, 2024
@seewoo5 seewoo5 self-assigned this Jul 30, 2024
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github-actions bot commented Jul 30, 2024

PR summary 024a80ca52

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ disjoint_normalizedFactors
+ disjoint_primeFactors
+ mul_primeFactors_disjUnion
+ radical_mul
+ radical_ne_zero
+ radical_neg
+ radical_neg_one

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

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

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

@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the blocked-by-other-PR This PR depends on another PR to Mathlib (this label is automatically managed by a bot) label Jul 30, 2024
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seewoo5 commented Jul 30, 2024

@erdOne Thank you for the reviews! It seems that most of them are for #14873. Could you leave the comments there? Then I'll updated in that PR accordingly.

@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Aug 5, 2024
-- Theorems for commutative rings

-- TODO: This holds for "nontrivial" monoids - do not need ring assumption.
theorem radical_ne_zero (a : R) : radical a ≠ 0 := by
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Yes, please state it in the generality that works.

rw [Finset.prod_disjUnion (disjoint_primeFactors hc)]

theorem radical_neg {a : R} : radical (-a) = radical a :=
neg_one_mul a ▸ (radical_eq_of_associated <| associated_unit_mul_left a (-1) isUnit_one.neg)
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I thought I added a lemma that a and -a are associated at some point. Can you please look for it?

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I'm looking at Algebra.Associated.Basic now, and I can find neg_left or neg_right which can be used combined with rfl, but not exactly something like Associated (-a) a. Should I look for different file?

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radical_eq_of_associated (.neg_right .rfl) (or some thing similar; not tested) is still shorter than this though.

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@erdOne Just updated - radical_eq_of_associated Associated.rfl.neg_left worked!

@Ruben-VandeVelde Ruben-VandeVelde added the awaiting-author A reviewer has asked the author a question or requested changes label Sep 11, 2024
@seewoo5 seewoo5 removed the awaiting-author A reviewer has asked the author a question or requested changes label Oct 7, 2024
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seewoo5 commented Oct 14, 2024

@Ruben-VandeVelde Hi, let me know if there are anything that I may update, thanks!

rw [Finset.prod_disjUnion (disjoint_primeFactors hc)]

theorem radical_neg {a : R} : radical (-a) = radical a :=
neg_one_mul a ▸ (radical_eq_of_associated <| associated_unit_mul_left a (-1) isUnit_one.neg)
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radical_eq_of_associated (.neg_right .rfl) (or some thing similar; not tested) is still shorter than this though.

@erdOne erdOne added the awaiting-author A reviewer has asked the author a question or requested changes label Oct 17, 2024
@seewoo5 seewoo5 removed the awaiting-author A reviewer has asked the author a question or requested changes label Oct 19, 2024
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bors d+

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mathlib-bors bot commented Oct 26, 2024

✌️ seewoo5 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

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seewoo5 commented Oct 26, 2024

bors r+

mathlib-bors bot pushed a commit that referenced this pull request Oct 26, 2024
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mathlib-bors bot commented Oct 26, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(RingTheory/Radical): Theorems for coprime elements + alpha [Merged by Bors] - feat(RingTheory/Radical): Theorems for coprime elements + alpha Oct 26, 2024
@mathlib-bors mathlib-bors bot closed this Oct 26, 2024
@mathlib-bors mathlib-bors bot deleted the feature/element-radical-coprime branch October 26, 2024 17:54
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