Theorems · Theorem · commutative algebra
HomogeneousLocalization.Away.mk_surjective
∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A]
[inst_2 : AddSubgroupClass σ A] [inst_3 : AddCommMonoid ι] [inst_4 : DecidableEq ι] (𝒜 : ι → σ)
[inst_5 : GradedRing 𝒜] {f : A} {d : ι} (hf : f ∈ 𝒜 d) (x : HomogeneousLocalization.Away 𝒜 f),
∃ n a, ∃ (ha : a ∈ 𝒜 (n • d)), HomogeneousLocalization.Away.mk 𝒜 hf n a ha = x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidstatement and proof · cited by 12,281
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- Submonoid.powersproof · cited by 408
- AddSubgroupClassstatement and proof · cited by 240
- ZeroMemClass.zero_memproof · cited by 162
- Localization.mkproof · cited by 110
- HomogeneousLocalization.Awaystatement and proof · cited by 105
- HomogeneousLocalization.NumDenSameDegproof · cited by 78
- HomogeneousLocalizationproof · cited by 69
- HomogeneousLocalization.mkproof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.awayToSection_comp_appLEproof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2