Theorems · Theorem · algebraic geometry
PrimeSpectrum.vanishingIdeal_eq_top_iff
∀ {R : Type u} [inst : CommSemiring R] {s : Set (PrimeSpectrum R)}, PrimeSpectrum.vanishingIdeal s = ⊤ ↔ s = ∅- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Idealstatement · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- top_le_iffproof · cited by 175
- PrimeSpectrum.zeroLocusproof · cited by 164
- Set.subset_empty_iffproof · cited by 40
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- Submodule.top_coeproof · cited by 8
- PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdealproof · cited by 3
- PrimeSpectrum.zeroLocus_univproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.