Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_eq_iff
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R},
PrimeSpectrum.zeroLocus ↑I = PrimeSpectrum.zeroLocus ↑J ↔ I.radical = J.radical- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 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
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- Ideal.radicalstatement and proof · cited by 121
- PrimeSpectrum.vanishingIdealproof · cited by 36
- PrimeSpectrum.zeroLocus_radicalproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopenproof · cited by 2
- PrimeSpectrum.exists_isClosed_singleton_of_isJacobsonRingproof · cited by 1
- ModuleCat.exists_isRegular_of_exists_subsingleton_extproof · cited by 1