Theorems · Theorem · algebraic geometry
PrimeSpectrum.isRadical_vanishingIdeal
∀ {R : Type u} [inst : CommSemiring R] (s : Set (PrimeSpectrum R)), (PrimeSpectrum.vanishingIdeal s).IsRadical- Cited by
- 1 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.
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
- Idealproof · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.vanishingIdealstatement and proof · cited by 36
- Ideal.IsRadicalstatement and proof · cited by 30
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 7
- Ideal.radical_isRadicalproof · cited by 7
- PrimeSpectrum.vanishingIdeal_closureproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrimeproof · cited by 1