Theorems · Theorem · algebraic geometry
PrimeSpectrum.mem_vanishingIdeal
∀ {R : Type u} [inst : CommSemiring R] (t : Set (PrimeSpectrum R)) (f : R),
f ∈ PrimeSpectrum.vanishingIdeal t ↔ ∀ x ∈ t, f ∈ x.asIdeal- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 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.
Cites9
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
- Idealstatement · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealstatement and proof · cited by 333
- SetLike.mem_coeproof · cited by 302
- Set.mem_ofPred_eqproof · cited by 122
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- PrimeSpectrum.coe_vanishingIdealproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 7
- PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdealproof · cited by 3
- MvPolynomial.vanishingIdeal_pointToPointproof · cited by 0
- PrimeSpectrum.sup_vanishingIdeal_leproof · cited by 0