Theorems · Definition · commutative algebra
IsDedekindDomain.HeightOneSpectrum.equivMaximalSpectrum
{R : Type u_1} →
[inst : CommRing R] → [IsDedekindDomain R] → ¬IsField R → IsDedekindDomain.HeightOneSpectrum R ≃ MaximalSpectrum RAn equivalence between the height one and maximal spectra for rings of Krull dimension 1.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
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
- Equivstatement · cited by 8,337
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
- IsFieldstatement and proof · cited by 103
- MaximalSpectrumstatement and proof · cited by 73
- MaximalSpectrum.asIdealproof · cited by 58
Cited by2
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.ideal_ne_top_iff_existsproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_botproof · cited by 0