Theorems · Theorem · algebraic geometry
PrimeSpectrum.vanishingIdeal_isIrreducible
∀ {R : Type u} [inst : CommSemiring R], PrimeSpectrum.vanishingIdeal '' {s | IsIrreducible s} = {P | P.IsPrime}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 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.
Cites17
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.coeproof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Set.extproof · cited by 2,266
- Ideal.IsPrimestatement and proof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusproof · cited by 164
- IsIrreduciblestatement and proof · cited by 59
- PrimeSpectrum.vanishingIdealstatement and proof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.vanishingIdeal_isClosed_isIrreducibleproof · cited by 1