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[Merged by Bors] - feat(RingTheory/Radical): Theorems for coprime elements + alpha #15331
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PR summary 024a80ca52Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Mathlib/RingTheory/Radical.lean
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-- Theorems for commutative rings | ||
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-- 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.
Mathlib/RingTheory/Radical.lean
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rw [Finset.prod_disjUnion (disjoint_primeFactors hc)] | ||
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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!
Co-authored-by: Ruben Van de Velde <[email protected]>
@Ruben-VandeVelde Hi, let me know if there are anything that I may update, thanks! |
Mathlib/RingTheory/Radical.lean
Outdated
rw [Finset.prod_disjUnion (disjoint_primeFactors hc)] | ||
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||
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.
Co-authored-by: Andrew Yang <[email protected]>
…er-community/mathlib4 into feature/element-radical-coprime
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bors d+
✌️ seewoo5 can now approve this pull request. To approve and merge a pull request, simply reply with |
Co-authored-by: Johan Commelin <[email protected]>
bors r+ |
Co-authored-by: Jineon Baek <[email protected]> Co-authored-by: Seewoo Lee <[email protected]>
Pull request successfully merged into master. Build succeeded: |
More theorems on element radical, especially multiplicativity of radical for coprime elements.
radical
toUniqueFactorizationDomain
#15826