Theorems · Theorem · commutative algebra
Subsemiring.isHomogeneous_iff_forall_subset
∀ {ι : Type u_1} {σ : Type u_2} {A : Type u_3} [inst : AddMonoid ι] [inst_1 : Semiring A] [inst_2 : SetLike σ A]
[inst_3 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_4 : DecidableEq ι] [inst_5 : GradedRing 𝒜] (R : Subsemiring A),
DirectSum.SetLike.IsHomogeneous 𝒜 R ↔ ∀ (i : ι), ↑R ⊆ ⇑(GradedRing.proj 𝒜 i) ⁻¹' ↑R- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement · cited by 8,199
- Set.preimagestatement · cited by 4,946
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- Subsemiringstatement and proof · cited by 456
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- GradedRing.projstatement · cited by 23
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