Theorems · Theorem · algebraic geometry
PrimeSpectrum.vanishingIdeal_closure
∀ {R : Type u} [inst : CommSemiring R] (t : Set (PrimeSpectrum R)),
PrimeSpectrum.vanishingIdeal (closure t) = PrimeSpectrum.vanishingIdeal t- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 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
- Idealstatement · cited by 4,748
- closurestatement · cited by 1,254
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- GaloisConnection.u_l_u_eq_uproof · cited by 17
- PrimeSpectrum.gcproof · cited by 14
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.vanishingIdeal_mem_minimalPrimesproof · cited by 2
- PrimeSpectrum.vanishingIdeal_isClosed_isIrreducibleproof · cited by 1
- PrimeSpectrum.isRadical_vanishingIdealproof · cited by 1