[Merged by Bors] - feat(PrimeSpectrum): Clopens in spectra of CommSemirings#20533
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alreadydone wants to merge 27 commits intomasterfrom
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[Merged by Bors] - feat(PrimeSpectrum): Clopens in spectra of CommSemirings#20533alreadydone wants to merge 27 commits intomasterfrom
alreadydone wants to merge 27 commits intomasterfrom
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PR summary 7dad3e79d1
|
| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.Algebra.Group.Idempotent | 126 | 127 | +1 (+0.79%) |
| Mathlib.RingTheory.Spectrum.Prime.Topology | 1616 | 1618 | +2 (+0.12%) |
Import changes for all files
| Files | Import difference |
|---|---|
4 filesMathlib.Algebra.Group.Idempotent Mathlib.Algebra.GroupWithZero.Idempotent Mathlib.Algebra.Order.Ring.Idempotent Mathlib.Algebra.Ring.Idempotent |
1 |
90 filesMathlib.Algebra.Category.Ring.Under.Limits Mathlib.AlgebraicGeometry.AffineScheme Mathlib.AlgebraicGeometry.AffineSpace Mathlib.AlgebraicGeometry.Cover.MorphismProperty Mathlib.AlgebraicGeometry.Cover.Open Mathlib.AlgebraicGeometry.Cover.Over Mathlib.AlgebraicGeometry.Fiber Mathlib.AlgebraicGeometry.FunctionField Mathlib.AlgebraicGeometry.GammaSpecAdjunction Mathlib.AlgebraicGeometry.GluingOneHypercover Mathlib.AlgebraicGeometry.Gluing Mathlib.AlgebraicGeometry.IdealSheaf Mathlib.AlgebraicGeometry.Limits Mathlib.AlgebraicGeometry.Modules.Presheaf Mathlib.AlgebraicGeometry.Modules.Sheaf Mathlib.AlgebraicGeometry.Modules.Tilde Mathlib.AlgebraicGeometry.Morphisms.AffineAnd Mathlib.AlgebraicGeometry.Morphisms.Affine Mathlib.AlgebraicGeometry.Morphisms.Basic Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion Mathlib.AlgebraicGeometry.Morphisms.Constructors Mathlib.AlgebraicGeometry.Morphisms.Etale Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation Mathlib.AlgebraicGeometry.Morphisms.FiniteType Mathlib.AlgebraicGeometry.Morphisms.Finite Mathlib.AlgebraicGeometry.Morphisms.Flat Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified Mathlib.AlgebraicGeometry.Morphisms.Immersion Mathlib.AlgebraicGeometry.Morphisms.Integral Mathlib.AlgebraicGeometry.Morphisms.IsIso Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion Mathlib.AlgebraicGeometry.Morphisms.Preimmersion Mathlib.AlgebraicGeometry.Morphisms.Proper Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties Mathlib.AlgebraicGeometry.Morphisms.Separated Mathlib.AlgebraicGeometry.Morphisms.Smooth Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen Mathlib.AlgebraicGeometry.Noetherian Mathlib.AlgebraicGeometry.OpenImmersion Mathlib.AlgebraicGeometry.Over Mathlib.AlgebraicGeometry.PointsPi Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme Mathlib.AlgebraicGeometry.Properties Mathlib.AlgebraicGeometry.PullbackCarrier Mathlib.AlgebraicGeometry.Pullbacks Mathlib.AlgebraicGeometry.RationalMap Mathlib.AlgebraicGeometry.ResidueField Mathlib.AlgebraicGeometry.Restrict Mathlib.AlgebraicGeometry.Scheme Mathlib.AlgebraicGeometry.Sites.BigZariski Mathlib.AlgebraicGeometry.Sites.Etale Mathlib.AlgebraicGeometry.Sites.MorphismProperty Mathlib.AlgebraicGeometry.Sites.Representability Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski Mathlib.AlgebraicGeometry.Sites.Small Mathlib.AlgebraicGeometry.Spec Mathlib.AlgebraicGeometry.SpreadingOut Mathlib.AlgebraicGeometry.Stalk Mathlib.AlgebraicGeometry.StructureSheaf Mathlib.AlgebraicGeometry.ValuativeCriterion Mathlib.RingTheory.Frobenius Mathlib.RingTheory.HopkinsLevitzki Mathlib.RingTheory.Ideal.GoingDown Mathlib.RingTheory.Ideal.Height Mathlib.RingTheory.Jacobson.Artinian Mathlib.RingTheory.RingHom.Flat Mathlib.RingTheory.RingHom.Unramified Mathlib.RingTheory.Smooth.Locus Mathlib.RingTheory.Spectrum.Maximal.Topology Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity Mathlib.RingTheory.Spectrum.Prime.Chevalley Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet Mathlib.RingTheory.Spectrum.Prime.FreeLocus Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC Mathlib.RingTheory.Spectrum.Prime.Jacobson Mathlib.RingTheory.Spectrum.Prime.Module Mathlib.RingTheory.Spectrum.Prime.Noetherian Mathlib.RingTheory.Spectrum.Prime.Polynomial Mathlib.RingTheory.Spectrum.Prime.TensorProduct Mathlib.RingTheory.Spectrum.Prime.Topology Mathlib.RingTheory.Unramified.LocalRing Mathlib.RingTheory.Unramified.Locus |
2 |
Declarations diff
+ basicOpen_eq_zeroLocus_of_mul_add
+ basicOpen_le_basicOpen_iff_algebraMap_isUnit
+ eq_biUnion_of_isOpen
+ exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen
+ iff_eq_one_of_isUnit
+ isClopen_basicOpen_of_mul_add
+ isClopen_iff_mul_add
+ isClopen_iff_mul_add_zeroLocus
+ isNilpotent_iff_zero_mem_powers
+ mulZeroAddOneEquivClopens
+ subsingleton_iff
+ zeroLocus_eq_basicOpen_of_mul_add
++ algebraMap_isUnit_iff
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.
No changes to technical debt.
You can run this locally as
./scripts/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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ADedecker
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Jan 28, 2025
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Thanks for the review! Changes have been made accordingly. |
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✌️ alreadydone can now approve this pull request. To approve and merge a pull request, simply reply with |
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As this PR is labelled bors merge |
mathlib-bors bot
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We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements `(e,f)` such that `e * f = 0` and `e + f = 1`. This happens precisely when `![e,f]` is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.
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Build failed (retrying...): |
mathlib-bors bot
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Apr 6, 2025
We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements `(e,f)` such that `e * f = 0` and `e + f = 1`. This happens precisely when `![e,f]` is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.
Contributor
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Build failed (retrying...): |
mathlib-bors bot
pushed a commit
that referenced
this pull request
Apr 6, 2025
We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements `(e,f)` such that `e * f = 0` and `e + f = 1`. This happens precisely when `![e,f]` is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.
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Pull request successfully merged into master. Build succeeded: |
tannerduve
pushed a commit
that referenced
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May 13, 2025
We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements `(e,f)` such that `e * f = 0` and `e + f = 1`. This happens precisely when `![e,f]` is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.
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We show that clopens in a commutative semiring are in 1-1 correspondence with pairs of elements
(e,f)such thate * f = 0ande + f = 1. This happens precisely when![e,f]is a complete orthogonal family of idempotents. Not all idempotents in a comm. semiring has such a complement: for example, in the semiring {0, 0.5, 1} with sup as + and inf as *, 0.5 doesn't have a complement.