Theorems · Theorem · commutative algebra
Ideal.toIdeal_homogeneousHull_eq_iSup
∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : DecidableEq ι] [inst_2 : AddMonoid ι]
[inst_3 : SetLike σ A] [inst_4 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_5 : GradedRing 𝒜] (I : Ideal A),
(Ideal.homogeneousHull 𝒜 I).toIdeal = ⨆ i, Ideal.span (⇑(GradedRing.proj 𝒜 i) '' ↑I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- iSupstatement · cited by 2,415
- Set.extproof · cited by 2,266
- SetLikestatement and proof · cited by 1,084
- Ideal.spanstatement and proof · cited by 948
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.homogeneousHull_eq_iSupproof · cited by 0