Theorems · Theorem · commutative algebra
HomogeneousIdeal.toIdeal_homogeneousCore_eq_self
∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : Semiring A] [inst_1 : SetLike σ A]
[inst_2 : AddSubmonoidClass σ A] {𝒜 : ι → σ} [inst_3 : DecidableEq ι] [inst_4 : AddMonoid ι] [inst_5 : GradedRing 𝒜]
(I : HomogeneousIdeal 𝒜), Ideal.homogeneousCore 𝒜 I.toIdeal = I- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 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.homogeneousCorestatement and proof · cited by 11
- HomogeneousIdeal.extproof · cited by 7
- HomogeneousIdeal.isHomogeneousproof · cited by 6
- Ideal.IsHomogeneous.toIdeal_homogeneousCore_eq_selfproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.homogeneousCore.gcproof · cited by 2