Theorems · Theorem · commutative algebra
HomogeneousIdeal.homogeneousHull_toIdeal_eq_self
∀ {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 : HomogeneousIdeal 𝒜),
Ideal.homogeneousHull 𝒜 I.toIdeal = I- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- HomogeneousIdealstatement and proof · cited by 115
- HomogeneousIdeal.toIdealstatement and proof · cited by 105
- Ideal.homogeneousHullstatement and proof · cited by 8
- HomogeneousIdeal.isHomogeneousproof · cited by 6
- HomogeneousIdeal.toIdeal_injectiveproof · cited by 5
- Ideal.IsHomogeneous.toIdeal_homogeneousHull_eq_selfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.homogeneousHull.gcproof · cited by 1