Theorems · Definition · number theory
Rat.HeightOneSpectrum.natGenerator
{R : Type u_2} →
[inst : CommRing R] → [inst_1 : Algebra R ℚ] → [IsIntegralClosure R ℤ ℚ] → IsDedekindDomain.HeightOneSpectrum R → ℕIf v : HeightOneSpectrum R then natGenerator v is the generator in ℕ of the corresponding
ideal in ℤ.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Ideal.mapproof · cited by 692
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
- IsIntegralClosurestatement and proof · cited by 146
- Submodule.IsPrincipal.generatorproof · cited by 56
- Rat.IsIntegralClosure.intEquivproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Rat.HeightOneSpectrum.primesEquivproof · cited by 6
- Rat.HeightOneSpectrum.prime_natGeneratorstatement · cited by 1
- Rat.HeightOneSpectrum.span_natGeneratorstatement · cited by 1
- Rat.HeightOneSpectrum.natGenerator_dvd_iffstatement and proof · cited by 0
- Rat.HeightOneSpectrum.valuation_equiv_padicValuationproof · cited by 0
- Rat.HeightOneSpectrum.natGenerator.congr_simpstatement and proof · cited by 0