Theorems · Theorem · commutative algebra
Ideal.IsHomogeneous.iff_exists
∀ {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.IsHomogeneous 𝒜 I ↔ ∃ S, I = Ideal.span (Subtype.val '' S)- Cited by
- 2 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Submonoidstatement · cited by 3,086
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- Ideal.spanstatement and proof · cited by 948
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- GaloisInsertion.gcproof · cited by 137
- Ideal.IsHomogeneousstatement · cited by 30
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.IsHomogeneous.mulproof · cited by 0
- Ideal.IsHomogeneous.supproof · cited by 0