Theorems · Theorem · commutative algebra
HomogeneousLocalization.subsingleton
∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A] (𝒜 : ι → σ) {x : Submonoid A},
0 ∈ x → Subsingleton (HomogeneousLocalization 𝒜 x)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Submonoidstatement and proof · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- Localizationproof · cited by 270
- HomogeneousLocalizationstatement · cited by 69
- HomogeneousLocalization.val_injectiveproof · cited by 24
- Function.Injective.subsingletonproof · cited by 16
- IsLocalization.subsingletonproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.Away.mk_surjectiveproof · cited by 2
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.num_mem_carrier_iffproof · cited by 1
- AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjectiveproof · cited by 0
- HomogeneousLocalization.mk_eq_zero_of_denproof · cited by 0