Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_radical
∀ {R : Type u} [inst : CommSemiring R] (I : Ideal R), PrimeSpectrum.zeroLocus ↑I.radical = PrimeSpectrum.zeroLocus ↑I- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 6 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 · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- Idealstatement and proof · cited by 4,748
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusstatement · cited by 164
- Ideal.radicalstatement · cited by 121
- GaloisConnection.l_u_l_eq_lproof · cited by 19
- PrimeSpectrum.gcproof · cited by 14
- PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_eq_iffproof · cited by 3
- PrimeSpectrum.closure_range_comapproof · cited by 2
- PrimeSpectrum.zeroLocus_powproof · cited by 0
- PrimeSpectrum.isClosed_iff_zeroLocus_radical_idealproof · cited by 0
- PrimeSpectrum.isIrreducible_zeroLocus_iffproof · cited by 0
- PrimeSpectrum.zeroLocus_nilradicalproof · cited by 0