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removed imports
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import Mathlib.Order.KrullDimension
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import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
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import Mathlib.RingTheory.Ideal.Operations
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import Mathlib.LinearAlgebra.Finsupp
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import Mathlib.RingTheory.GradedAlgebra.Basic
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import Mathlib.RingTheory.GradedAlgebra.HomogeneousIdeal
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import Mathlib.Algebra.Module.GradedModule
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import Mathlib.RingTheory.Ideal.AssociatedPrime
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import Mathlib.RingTheory.Noetherian
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import Mathlib.RingTheory.Artinian
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import Mathlib.RingTheory.FiniteType
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import Mathlib.Order.Height
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import Mathlib.RingTheory.PrincipalIdealDomain
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import Mathlib.RingTheory.DedekindDomain.Basic
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import Mathlib.RingTheory.Ideal.Quotient
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import Mathlib.RingTheory.Localization.AtPrime
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import Mathlib.Order.ConditionallyCompleteLattice.Basic
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import Mathlib.Algebra.DirectSum.Ring
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import Mathlib.RingTheory.Ideal.LocalRing
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--import Mathlib
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import Mathlib.Algebra.MonoidAlgebra.Basic
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import Mathlib.Data.Finset.Sort
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import Mathlib.Order.JordanHolder
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import Mathlib.RingTheory.Ideal.Basic
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import Mathlib.RingTheory.Finiteness
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noncomputable def length ( A : Type _) (M : Type _)
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[CommRing A] [AddCommGroup M] [Module A M] := Set.chainHeight {M' : Submodule A M | M' < ⊤}
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