2023-06-12 12:34:51 -05:00
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import Mathlib.RingTheory.Ideal.Basic
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import Mathlib.RingTheory.Noetherian
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import Mathlib.RingTheory.Artinian
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import Mathlib.RingTheory.Ideal.Quotient
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import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
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2023-06-12 15:34:09 -05:00
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lemma quotientRing_is_Artinian (R : Type _) [CommRing R] (I : Ideal R) (IsArt : IsArtinianRing R):
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IsArtinianRing (R⧸I) := by sorry
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#check Ideal.IsPrime
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lemma IsPrimeMaximal (R : Type _) [CommRing R] (I : Ideal R) (IsArt : IsArtinianRing R) (isPrime : Ideal.IsPrime I) : Ideal.IsMaximal I := by sorry
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2023-06-12 12:34:51 -05:00
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-- Use Stacks project proof since it's broken into lemmas
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