Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_minimalPrimes
∀ (R : Type u) [inst : CommSemiring R], PrimeSpectrum.zeroLocus ∘ SetLike.coe '' minimalPrimes R = irreducibleComponents (PrimeSpectrum R)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 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.
Cites15
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
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- Set.image_compproof · cited by 142
- PrimeSpectrum.vanishingIdealproof · cited by 36
- irreducibleComponentsstatement and proof · cited by 35
- minimalPrimesstatement · cited by 32
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.vanishingIdeal_mem_minimalPrimesproof · cited by 2