Theorems · Theorem · number theory
Rat.HeightOneSpectrum.prime_natGenerator
∀ {R : Type u_2} [inst : CommRing R] [inst_1 : Algebra R ℚ] [inst_2 : IsIntegralClosure R ℤ ℚ]
(v : IsDedekindDomain.HeightOneSpectrum R), Nat.Prime (Rat.HeightOneSpectrum.natGenerator v)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 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
- Nat.Primestatement · cited by 2,059
- Ideal.mapproof · cited by 692
- Iff.notproof · cited by 489
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
- IsIntegralClosurestatement and proof · cited by 146
- RingEquiv.injectiveproof · cited by 39
- IsDedekindDomain.HeightOneSpectrum.ne_botproof · cited by 15
- Ideal.map_eq_bot_iff_of_injectiveproof · cited by 14
- Int.prime_iff_natAbs_primeproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Rat.HeightOneSpectrum.primesEquivproof · cited by 6
- Rat.HeightOneSpectrum.valuation_equiv_padicValuationproof · cited by 0