diff --git a/CommAlg/monalisa.lean b/CommAlg/monalisa.lean
index 717e95a..357578b 100644
--- a/CommAlg/monalisa.lean
+++ b/CommAlg/monalisa.lean
@@ -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)