Theorems · Theorem · commutative algebra
Ideal.toIdeal_homogeneousCore_le
∀ {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 : Ideal A), (Ideal.homogeneousCore 𝒜 I).toIdeal ≤ I- Cited by
- 2 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.
Cites9
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
- Idealstatement and proof · cited by 4,748
- 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
- HomogeneousIdeal.toIdealstatement · cited by 105
- Ideal.homogeneousCorestatement · cited by 11
- Ideal.homogeneousCore'_leproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.IsPrime.homogeneousCoreproof · cited by 1
- Ideal.IsHomogeneous.radical_eqproof · cited by 1