Theorems · Definition · number theory
Rat.HeightOneSpectrum.primesEquiv
{R : Type u_2} →
[inst : CommRing R] →
[inst_1 : Algebra R ℚ] →
[IsIntegralClosure R ℤ ℚ] → [IsDedekindDomain R] → IsDedekindDomain.HeightOneSpectrum R ≃ Nat.PrimesThe equivalence between height-one prime ideals of R and primes in ℕ.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Ideal.spanproof · cited by 948
- Ideal.mapproof · cited by 692
- IsDedekindDomainstatement and proof · cited by 668
- RingEquiv.symmproof · cited by 567
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Primeproof · cited by 277
- IsIntegralClosurestatement and proof · cited by 146
- Nat.Primesstatement and proof · cited by 63
- Rat.IsIntegralClosure.intEquivproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- Rat.HeightOneSpectrum.adicCompletion.padicEquivstatement and proof · cited by 5
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivstatement and proof · cited by 4
- Padic.adicCompletionEquivstatement and proof · cited by 2
- PadicInt.adicCompletionIntegersEquivstatement and proof · cited by 2
- Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_applystatement · cited by 1
- Rat.HeightOneSpectrum.valuation_equiv_padicValuationstatement and proof · cited by 0
- Rat.HeightOneSpectrum.withValEquivstatement · cited by 0
- PadicInt.coe_adicCompletionIntegersEquiv_applystatement and proof · cited by 0
- PadicInt.coe_adicCompletionIntegersEquiv_symm_applystatement and proof · cited by 0
- Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOnstatement and proof · cited by 0
- Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_applystatement and proof · cited by 0