Theorems · Definition · algebraic geometry
PrimeSpectrum.asIdeal
{R : Type u_1} → [inst : CommSemiring R] → PrimeSpectrum R → Ideal R- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Defs
- Cited by
- 333 results in Mathlib
- Foundations
- Depth 15 from the axioms, rests on 130 definitions · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
Cited by380
Results whose statement or proof uses this declaration.
- PrimeSpectrum.comapproof · cited by 199
- PrimeSpectrum.zeroLocusproof · cited by 164
- PrimeSpectrum.basicOpenproof · cited by 163
- Module.supportproof · cited by 52
- PrimeSpectrum.extstatement and proof · cited by 43
- Module.rankAtStalkproof · cited by 41
- PrimeSpectrum.vanishingIdealproof · cited by 36
- PrimeSpectrum.basicOpen_eq_zeroLocus_complproof · cited by 34
- PrimeSpectrum.PiLocalizationproof · cited by 20
- PrimeSpectrum.localization_away_comap_rangeproof · cited by 17
- PrimeSpectrum.zeroLocus_spanproof · cited by 17
- AlgebraicGeometry.StructureSheaf.Localizationsproof · cited by 15
Showing the 200 most cited of 380.