Theorems · Theorem · commutative algebra
HomogeneousLocalization.val_injective
∀ {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),
Function.Injective HomogeneousLocalization.val- Cited by
- 24 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, 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.
- CommRingstatement and proof · cited by 17,173
- Submonoidstatement and proof · cited by 3,086
- SetLikestatement and proof · cited by 1,084
- Localizationstatement · cited by 270
- Quotient.mk''proof · cited by 132
- HomogeneousLocalization.NumDenSameDegproof · cited by 78
- HomogeneousLocalizationstatement and proof · cited by 69
- HomogeneousLocalization.valstatement and proof · cited by 51
- Quotient.sound'proof · cited by 30
- Quotient.recOnSubsingleton₂'proof · cited by 1
Cited by24
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.ext_iff_valproof · cited by 7
- HomogeneousLocalization.subsingletonproof · cited by 5
- AlgebraicGeometry.Proj.awayMap_awayToSectionproof · cited by 2
- AlgebraicGeometry.Proj.awayToSection_comp_appLEproof · cited by 2
- HomogeneousLocalization.Away.mk_surjectiveproof · cited by 2
- HomogeneousLocalization.map_compproof · cited by 2
- HomogeneousLocalization.val_awayMap_eq_auxproof · cited by 2
- HomogeneousLocalization.awayMap_fromZeroRingHomproof · cited by 2
- HomogeneousLocalization.awayMap_mkproof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1