Theorems · Theorem · commutative algebra
Ideal.mem_homogeneousCore_of_homogeneous_of_mem
∀ {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} {x : A}, SetLike.IsHomogeneousElem 𝒜 x → x ∈ I → x ∈ Ideal.homogeneousCore 𝒜 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.
Cites10
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
- HomogeneousIdealstatement · cited by 115
- Ideal.subset_spanproof · cited by 86
- SetLike.IsHomogeneousElemstatement and proof · cited by 18
- Ideal.homogeneousCorestatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.IsPrime.homogeneousCoreproof · cited by 1