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Theorems · Definition · commutative algebra

HomogeneousLocalization.mk

{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} → HomogeneousLocalization.NumDenSameDeg 𝒜 x → HomogeneousLocalization 𝒜 x

Construct an element of HomogeneousLocalization 𝒜 x from a homogeneous fraction.

Defined in
Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization
Cited by
55 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext
Assumes
CommRingSetLike

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomogeneousLocalization.mk_surjective · cited by 14HomogeneousLocalization.m…HomogeneousLocalization.val_mk · cited by 14HomogeneousLocalization.v…HomogeneousLocalization.Away.mk · cited by 11Away.mkAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier · cited by 9FromSpec.carrierHomogeneousLocalization.fromZeroRingHom · cited by 7HomogeneousLocalization.f…AlgebraicGeometry.sectionInBasicOpen · cited by 6AlgebraicGeometry.section…AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier · cited by 5ToSpec.mk_mem_carrierAlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq · cited by 3Proj.toSpec_base_apply_eqHomogeneousLocalization.val_awayMap_mk · cited by 3HomogeneousLocalization.v…AlgebraicGeometry.Proj.awayMap_awayToSection · cited by 2Proj.awayMap_awayToSectionAlgebraicGeometry.Proj.awayToSection_comp_appLE · cited by 2Proj.awayToSection_comp_a…AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.denom_notMem · cited by 2carrier.denom_notMemAlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_mem · cited by 2carrier.zero_memHomogeneousLocalization.awayMapAux_mk · cited by 2HomogeneousLocalization.a…HomogeneousLocalization.awayMap_fromZeroRingHom · cited by 2HomogeneousLocalization.a…CommRing · cited by 17173CommRingSubmonoid · cited by 3086SubmonoidSetLike · cited by 1084SetLikeQuotient.mk'' · cited by 132Quotient.mk''HomogeneousLocalization.NumDenSameDeg · cited by 78HomogeneousLocalization.N…HomogeneousLocalization · cited by 69HomogeneousLocalizationHomogeneousLocalization.mkCITED BYCITES

Cites6

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Cited by60

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