Theorems · Theorem · algebraic geometry
PrimeSpectrum.isIrreducible_zeroLocus_iff_of_radical
∀ {R : Type u} [inst : CommSemiring R] (I : Ideal R),
I.IsRadical → (IsIrreducible (PrimeSpectrum.zeroLocus ↑I) ↔ I.IsPrime)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Ideal.spanproof · cited by 948
- Ideal.IsPrimestatement · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- Ideal.mul_mem_leftproof · cited by 107
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Ideal.mul_mem_rightproof · cited by 71
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrimeproof · cited by 1
- PrimeSpectrum.vanishingIdeal_isIrreducibleproof · cited by 1
- PrimeSpectrum.isIrreducible_zeroLocus_iffproof · cited by 0