Theorems · Theorem · algebraic geometry
PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdeal
∀ {R : Type u} [inst : CommSemiring R] (t : Set (PrimeSpectrum R)) (I : Ideal R),
t ⊆ PrimeSpectrum.zeroLocus ↑I ↔ I ≤ PrimeSpectrum.vanishingIdeal t- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 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.
Cites10
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
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- le_transproof · cited by 985
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- PrimeSpectrum.vanishingIdealstatement and proof · cited by 36
- PrimeSpectrum.mem_zeroLocusproof · cited by 7
- PrimeSpectrum.mem_vanishingIdealproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.gcproof · cited by 14
- PrimeSpectrum.zeroLocus_subset_zeroLocus_iffproof · cited by 2
- PrimeSpectrum.vanishingIdeal_eq_top_iffproof · cited by 0