Theorems · Theorem · algebraic geometry
PrimeSpectrum.vanishingIdeal_singleton
∀ {R : Type u} [inst : CommSemiring R] (x : PrimeSpectrum R), PrimeSpectrum.vanishingIdeal {x} = x.asIdeal- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 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
- Idealstatement · cited by 4,748
- iInfproof · cited by 1,690
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealstatement and proof · cited by 333
- iInf_congr_Propproof · cited by 218
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- iInf_iInf_eq_leftproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClosed_singleton_iff_isMaximalproof · cited by 8
- PrimeSpectrum.le_iff_mem_closureproof · cited by 1
- AlgebraicGeometry.genericPoint_eq_bot_of_affineproof · cited by 1
- AlgebraicGeometry.isField_stalk_of_closure_mem_irreducibleComponentsproof · cited by 1
- PrimeSpectrum.closure_singletonproof · cited by 0