Theorems · Theorem · algebraic geometry
PrimeSpectrum.vanishingIdeal_irreducibleComponents
∀ (R : Type u) [inst : CommSemiring R], PrimeSpectrum.vanishingIdeal '' irreducibleComponents (PrimeSpectrum R) = minimalPrimes R
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 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.
Cites20
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
- Set.ofPredproof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- IsClosedproof · cited by 1,639
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- Maximalproof · cited by 211
- Minimalproof · cited by 150
- Set.mem_ofPred_eqproof · cited by 122
- IsIrreducibleproof · cited by 59
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.vanishingIdeal_mem_minimalPrimesproof · cited by 2
- PrimeSpectrum.zeroLocus_minimalPrimesproof · cited by 1