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Merge pull request #25 from GTBarkley/leo

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Leo
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Leo Mayer 2023-06-12 13:05:57 -07:00 committed by GitHub
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8
CommAlg/krull.lean
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@ -1,4 +1,5 @@
import Mathlib.RingTheory.Ideal.Basic import Mathlib.RingTheory.Ideal.Operations
import Mathlib.RingTheory.FiniteType
import Mathlib.Order.Height import Mathlib.Order.Height
import Mathlib.RingTheory.PrincipalIdealDomain import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.RingTheory.DedekindDomain.Basic import Mathlib.RingTheory.DedekindDomain.Basic
@ -33,11 +34,12 @@ noncomputable instance : CompleteLattice (WithBot (ℕ∞)) := WithBot.WithTop.c
lemma krullDim_le_iff (R : Type) [CommRing R] (n : ℕ) : lemma krullDim_le_iff (R : Type) [CommRing R] (n : ℕ) :
iSup (λ I : PrimeSpectrum R => (height I : WithBot ℕ∞)) ≤ n ↔ iSup (λ I : PrimeSpectrum R => (height I : WithBot ℕ∞)) ≤ n ↔
∀ I : PrimeSpectrum R, (height I : WithBot ℕ∞) ≤ ↑n := by ∀ I : PrimeSpectrum R, (height I : WithBot ℕ∞) ≤ ↑n := iSup_le_iff (α := WithBot ℕ∞)
convert @iSup_le_iff (WithBot ℕ∞) (PrimeSpectrum R) inferInstance _ (↑n)
--some propositions that would be nice to be able to eventually --some propositions that would be nice to be able to eventually
lemma dim_eq_bot_iff : krullDim R = ⊥ ↔ Subsingleton R := sorry
lemma dim_eq_zero_iff_field [IsDomain R] : krullDim R = 0 ↔ IsField R := by sorry lemma dim_eq_zero_iff_field [IsDomain R] : krullDim R = 0 ↔ IsField R := by sorry
#check Ring.DimensionLEOne #check Ring.DimensionLEOne

6
CommAlg/resources.lean
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@ -7,6 +7,7 @@ useful lemmas and definitions
import Mathlib.RingTheory.Ideal.Basic import Mathlib.RingTheory.Ideal.Basic
import Mathlib.RingTheory.Noetherian import Mathlib.RingTheory.Noetherian
import Mathlib.RingTheory.Artinian import Mathlib.RingTheory.Artinian
import Mathlib.RingTheory.FiniteType
import Mathlib.Order.Height import Mathlib.Order.Height
import Mathlib.RingTheory.MvPolynomial.Basic import Mathlib.RingTheory.MvPolynomial.Basic
import Mathlib.RingTheory.Ideal.Over import Mathlib.RingTheory.Ideal.Over
@ -59,6 +60,11 @@ variable (I : Ideal R)
--Theorems relating primes of a ring to primes of a quotient --Theorems relating primes of a ring to primes of a quotient
#check PrimeSpectrum.range_comap_of_surjective #check PrimeSpectrum.range_comap_of_surjective
--There's a lot of theorems about finite-type algebras
#check Algebra.FiniteType.polynomial
#check Algebra.FiniteType.mvPolynomial
#check Algebra.FiniteType.of_surjective
-- There is a notion of short exact sequences but the number of theorems are lacking -- There is a notion of short exact sequences but the number of theorems are lacking
-- For example, I couldn't find anything saying that for a ses 0 -> A -> B -> C -> 0 -- For example, I couldn't find anything saying that for a ses 0 -> A -> B -> C -> 0
-- of R-modules, A and C being FG implies that B is FG -- of R-modules, A and C being FG implies that B is FG