Theorems · Theorem · commutative algebra
IsArtinianRing.primeSpectrumEquivMaximalSpectrum_apply_asIdeal
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsArtinianRing R] (I : PrimeSpectrum R),
(IsArtinianRing.primeSpectrumEquivMaximalSpectrum I).asIdeal = I.asIdeal- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsArtinianRing
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivstatement · cited by 8,337
- Idealstatement · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealstatement · cited by 333
- IsArtinianRingstatement and proof · cited by 98
- MaximalSpectrumstatement · cited by 73
- MaximalSpectrum.asIdealstatement and proof · cited by 58
- IsArtinianRing.primeSpectrumEquivMaximalSpectrumstatement and proof · cited by 7
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