Theorems · Theorem · commutative algebra
IsArtinianRing.quotNilradicalEquivPi_symm_apply
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsArtinianRing R] (a : (I : MaximalSpectrum R) → R ⧸ I.asIdeal),
(IsArtinianRing.quotNilradicalEquivPi R).symm a =
(Ideal.quotientEquivAlgOfEq R ⋯) ((Ideal.quotientInfRingEquivPiQuotient MaximalSpectrum.asIdeal ⋯).symm a)- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsArtinianRing
Around this declaration
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Cites18
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
- Idealstatement · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- iInfstatement · cited by 1,690
- AlgEquivstatement · cited by 1,681
- RingEquivstatement · cited by 1,147
- AlgEquiv.symmstatement · cited by 615
- RingEquiv.symmstatement and proof · cited by 567
- IsArtinianRingstatement and proof · cited by 98
- MaximalSpectrumstatement and proof · cited by 73
- MaximalSpectrum.asIdealstatement and proof · cited by 58
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