Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_subset_zeroLocus_iff
∀ {R : Type u} [inst : CommSemiring R] (I J : Ideal R),
PrimeSpectrum.zeroLocus ↑I ⊆ PrimeSpectrum.zeroLocus ↑J ↔ J ≤ I.radical- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 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 · 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
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- Ideal.radicalstatement and proof · cited by 121
- PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 7
- PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdealproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_subset_zeroLocus_singleton_iffproof · cited by 1
- ModuleCat.subsingleton_ext_of_exists_isRegularproof · cited by 1