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Theorems · Theorem · commutative algebra

HomogeneousLocalization.mk_surjective

∀ {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.Surjective HomogeneousLocalization.mk
Defined in
Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization
Cited by
14 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext
Assumes
CommRingSetLike

Around this declaration

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

AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq · cited by 3Proj.toSpec_base_apply_eqAlgebraicGeometry.Proj.awayMap_awayToSection · cited by 2Proj.awayMap_awayToSectionHomogeneousLocalization.Away.mk_surjective · cited by 2Away.mk_surjectiveHomogeneousLocalization.val_localRingHom · cited by 2HomogeneousLocalization.v…HomogeneousLocalization.map_comp · cited by 2HomogeneousLocalization.m…AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec · cited by 1ProjIsoSpecTopComponent.t…HomogeneousLocalization.range_awayMapAux_subset · cited by 1HomogeneousLocalization.r…HomogeneousLocalization.Away.span_mk_prod_pow_eq_top · cited by 1Away.span_mk_prod_pow_eq_…AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply · cited by 1Proj.awayToSection_applyHomogeneousLocalization.isUnit_iff_isUnit_val · cited by 1HomogeneousLocalization.i…HomogeneousLocalization.map_id · cited by 1HomogeneousLocalization.m…AlgebraicGeometry.Proj.localRingHom_comp_stalkIso · cited by 1Proj.localRingHom_comp_st…AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime · cited by 0Proj.isLocalization_atPri…AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective · cited by 0Proj.lift_awayMapₐ_awayMa…CommRing · cited by 17173CommRingSubmonoid · cited by 3086SubmonoidSetLike · cited by 1084SetLikeHomogeneousLocalization.NumDenSameDeg · cited by 78HomogeneousLocalization.N…HomogeneousLocalization · cited by 69HomogeneousLocalizationHomogeneousLocalization.mk · cited by 55HomogeneousLocalization.mkQuotient.mk''_surjective · cited by 19Quotient.mk''_surjectiveHomogeneousLocalization.mk_su…CITED BYCITES

Cites7

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Cited by14

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