SinTan1729/comm_alg
1
0
Fork 0
mirror of https://github.com/GTBarkley/comm_alg.git synced 2024-10-16 19:43:55 -05:00
Code Issues Projects Releases Packages Wiki Activity

added homogeneous graded ideal

Browse source
This commit is contained in:
monula95 dutta 2023-06-14 20:01:06 +00:00
parent a1888c51e6
commit 6f6547c7a4
1 changed files with 10 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

10
CommAlg/monalisa.lean
View file

@ -93,3 +93,13 @@ lemma ass_graded (𝒜 : ℤ → Type _) (𝓜 : ℤ → Type _)
(p : associatedPrimes (⨁ i, 𝒜 i) (⨁ i, 𝓜 i)) : (HomogeneousMax 𝒜 p) := by
sorry
lemma Associated_prime_of_graded_is_graded
(𝒜 : ℤ → Type _) (𝓜 : ℤ → Type _)
[∀ i, AddCommGroup (𝒜 i)] [∀ i, AddCommGroup (𝓜 i)]
[DirectSum.GCommRing 𝒜] [DirectSum.Gmodule 𝒜 𝓜]
(p : associatedPrimes (⨁ i, 𝒜 i) (⨁ i, 𝓜 i))
: (Ideal.IsHomogeneous' 𝒜 p) ∧ ((∃ (i : ℤ ), ∃ (x : 𝒜 i), p = (Submodule.span (⨁ i, 𝒜 i) {DirectSum.of x i}).annihilator)) := by
sorry
def standard_graded (𝒜 : ℤ → Type _) [∀ i, AddCommGroup (𝒜 i)] [DirectSum.GCommRing 𝒜] (I : Ideal (⨁ i, 𝒜 i)) := (⨁ i, 𝒜 i)