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Merge pull request #21 from GTBarkley/jayden

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add lemmas
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Jidong Wang 2023-06-12 10:14:26 -07:00 committed by GitHub
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comm_alg/jayden(krull-dim-zero).lean
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import Mathlib.RingTheory.Ideal.Basic
import Mathlib.RingTheory.Noetherian
import Mathlib.Order.KrullDimension
import Mathlib.RingTheory.Artinian
import Mathlib.RingTheory.Ideal.Quotient
import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
lemma dim_zero_Noetherian_is_Artinian (R : Type _) (IsNoetherianRing R) (krull_dim R = 0) : IsArtinianRing R := by sorry
variable {R : Type _} [CommRing R]
-- Use Stacks project proof since it's broken into lemmas
-- Repeats the definition by Monalisa
noncomputable def length : krullDim (Submodule _ _)
-- The following is Stacks Lemma 10.60.5
lemma dim_zero_Noetherian_iff_Artinian (R : Type _) [CommRing R] :
IsNoetherianRing R ∧ krull_dim R = 0 ↔ IsArtinianRing R := by
sorry
#check IsNoetherianRing
-- The following is Stacks Lemma 10.53.6
lemma IsArtinian_iff_finite_length : IsArtinianRing R ↔ ∃ n : ℕ, length R R ≤ n := by sorry