Theorems · Definition · commutative algebra
IsArtinianRing.primeSpectrumEquivMaximalSpectrum
{R : Type u_1} → [inst : CommRing R] → [IsArtinianRing R] → PrimeSpectrum R ≃ MaximalSpectrum RThe prime spectrum is in bijection with the maximal spectrum.
- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsArtinianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- IsArtinianRingstatement and proof · cited by 98
- MaximalSpectrumstatement and proof · cited by 73
- MaximalSpectrum.asIdealproof · cited by 58
Cited by8
Results whose statement or proof uses this declaration.
- Algebra.FormallyEtale.equivPiOfIsSepClosedproof · cited by 3
- Algebra.FormallyEtale.equivPiOfIsSepClosed_comapproof · cited by 0
- Algebra.FormallyEtale.equivPiOfIsSepClosed_self_applyproof · cited by 0
- IsArtinianRing.primeSpectrumEquivMaximalSpectrum_apply_asIdealstatement and proof · cited by 0
- IsArtinianRing.primeSpectrumEquivMaximalSpectrum.congr_simpstatement and proof · cited by 0
- IsArtinianRing.primeSpectrumEquivMaximalSpectrum_comp_asIdealstatement · cited by 0
- IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_comp_asIdealstatement · cited by 0
- IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_apply_asIdealstatement and proof · cited by 0